I've been running a Saiga-12 since around the end of the AWB. I can't remember exactly when I got it, but it was back when they were about $199, and unpopular, right about when the very first conversions were being performed. I had been craving an "action shooting" style shotgun, and was absolutely nuts for a mag-fed shotgun. I had seen the gun around in local gun shows, and had a couple of dollars in my pocket from a college summer internship.
While it was easy to part with two hundred bucks, and accept whatever it was I was getting for the money, I would advise a different approach given the increased price for the current Saiga-12s. The problem is that while the AK platform is generally considered to be over-gassed in rifle format, shotguns produce far less gas pressure. The Saiga-12 has gas ports in the barrel. Gas flowing from the ports impinges on a "puck", which then acts on the Saiga-12s "gas piston". Gas will flow while the wad/shot is past the ports until it exits the barrel. During the course of Saiga-12 production, the number and diameter of the gas ports has varied. Additionally, multiple barrel lengths have been produced. I'm aware of the 22", the 19", and I think that there's another couple that have been made. Finally, there have been many observed instances where poor manufacturing practices have led to guns with incorrectly drilled gas ports, or gas ports that have been accidentally blocked by barrel/gas block hardware. If you want to cut down the barrel for a shorter gun, the gas ports must be given due attention and modification.
If you can, the first option would be to see if you can get a Saiga-12 seller to give you a 1-3 day evaluation period. If not, another good option would be to try to purchase a Saiga-12 from a gun shop that you have some type of established relationship with. You can head on over to the Saiga-12 forums, where there is a good amount of information on the correct number and size of gas ports for given barrels and loads. If at all possible, get the gunshop/seller to strip the gun down until it is possible to inspect the gas ports. It is extremely important to consider what kind of ammo you would want to shoot out of a Saiga-12, before attempting to acquiring one. It would be extremely unlikely, but slightly possible, to purchase a Saiga-12 that would cycle the popular low-cost big box "trap and skeet" light loads. The best bet on that would be a 4-port gun with a long barrel, and further, that the ports be on the bigger side. It could be considered inappropriate to purchase a Saiga-12 with an evaluation period and return the gun because it wouldn't cycle the "trap and skeet" loads, while a gun that can't cycle buck and slug would be due for a return.
There are options that are less dramatic than getting a Saiga-12 sent off for a conversion that costs the same amount as the purchase price of the gun. However, be aware that a Saiga-12 converted by an experienced builder is a really, really nice option. I shot mine for years in the stock configuration before getting it converted, and it really was a different and better gun when it came back. Please also be aware of the magazine capacity legal issues, if you have an unconverted gun. If you have a converted gun, check the parts count yourself to make sure you're GTG before sticking big mags in the gun. If you're going to be sticking to the stock configuration, there are certain affordable/easy modifications that can be made to get a gun that'll cycle the widest variety of loads as reliably as possible. There are many places to go for Saiga-12 parts, I will mention CSS as a good place to look around to see what is available.
1) The five-port gas plug that you mentioned earlier is extremely useful. No matter what else you may do to your Saiga-12, load versatility is a unique and (to me, at least) important feature of shotguns in general. The more gas control you have, the wider variety of loads you will be able to shoot. This is an easy part to change out, and can be done by hand in seconds.
2) Reduced power mainspring. With the reduced power mainspring and the adjustable gas plug, you will have 10 different settings to cycle ammo.
With those two options, you'll be doing the best that you can do with a simple field-strip and an absolutely minimal additional financial expenditure to get a gun that'll run as well as possible with the widest variety of ammunition.
3) Polished bolt and carrier. While there are a couple of places that can do this, and you can certainly give the polishing a go yourself, my recommendation is send the bolt to "Pauly", whose work can be found over on the Saiga-12 forums. The polish and chrome serves to make the gun cycle as smoothly as possible, reducing the total force required to cycle the gun. Additionally, the smooth, recontoured bolt will greatly ease inserting a magazine into the gun with the bolt forward. The bolt service includes insurance in an amount sufficient to purchase another gun should the bolt be lost in the mail.
Soooo, what about the MK 1919? I've got an AR, and it is a much more ergonomic gun than an AK. However, while the Saiga-12 is a true AK action in every sense except the gas puck, (which I understand is enough for plenty of people not to consider it a "true AK"), the MK 1919 is extremely similar to the Remington 1100. I have experience with the Remington 1100 in the shortened barrel, extended magazine variant. The shooter who owned the gun used a Remington 1100 for shooting his clay games, and wanted an action shotgun that was as similar to his clay gun as possible. The 1100 is a good shotgun, but it is in no sense as rugged, simple, or durable as the Saiga-12 AK action. However, given the above discussion about Saiga-12 production variability, it is likely that the MK 1919 will be more reliable in an out-of-the box configuration. Will this make a difference you?
The Saiga-12 has an extreme amount of aftermarket accessories, but the shooting community does appear very excited about the MK 1919, and aftermarket parts are either available or in design. Magazines for the MK 1919 are not as high in capacity or as diverse in design as the Saiga-12 magazines, but if the MK 1919 is successful, expect an increase in magazine choices and availability for the MK 1919.
To compare the guns, it is important to establish baseline configurations. For the purposes of this discussion, I will spec out three levels of Saiga-12:
Level 1: 5 port gas plug, reduced power mainspring, optional polished/chromed bolt. This gets you the best near-stock Saiga-12 for as little money as possible above and beyond the initial purchase price.
Level 2: Level 1 plus conversion to conventional AK furniture. (grip and buttstock, optional forearm) This level gets you the greatly improved ergonomics of the AK buttstock (there are tons of quality adapters to permit the use of AR stocks/grips, if that's where your preference lies). At this level, you should expect that the barrel will be shortened to your specification, and that any gas port issues would be resolved, which should make the gun extremely reliable. Skill and experience in achieving an extremely reliable barrel/gas port configuration is why my advice is to go to an experienced Saiga-12 builder (not just someone who has AK experience) for the Level 2 configuration. In my experience, the conversion does a lot to ease magazine changes/reloading. If you go this far, it is usually worth adding better sights (lots of options here, pick what you like) and a retaining plate in place of the shepard's crook (Cheap part, great for making the Saiga-12 much easier to detail strip). The cost of these conversions is dependent on exactly what you want done, but expect to pay in the $600-1000 range. You can get along with the standard AK safety and mag release, but an upgrade to one of the "shelf" style safety levers is for your trigger finger is typically very affordable (similar price to the 5-port gas plug) and does wonders for safety manipulation. Practice mag changes with the bolt back, then start practicing them with the bolt forward. It is at this point that you will probably either want a polished bolt, or be smugly satisfied that you have one. Especially without the polished bolt, fast reloads at this stage are a highly perishable skill.
Level 3: Level 2 plus anything else you might want. Here's where the guns get crazy. R and R target's Saiga-12s are great examples of Level 3 guns. At this point, you can get AR-style safeties, mag wells, and mag releases, or you can get advanced AK/Saiga-12 specific safeties, magazine well modifications, and mag releases. Guns set-up for use with drums typically retain the rock-and-lock magazine loading techniques, while guns set up for stick magazines will typically include either a speed-loading plate (way cool, and the magazines stay stock) or a magazine well that allows you to insert the magazines in an AR-style fashion (way, way cool, but the magazines must be modified to work in the mag well, and this really should be done by a professional). A properly set-up Level 3 gun is monstrously reliable, highly ergonomic, and fast to reload. However, the additional cost to get a box-stock Saiga to Level 3 can be twice as expensive as a Level 2 conversion, and sometimes more.
Considering that the MK 1919 already comes in pistol-grip configuration, I am defining two Levels of MK 1919
Level 2: Stock gun. The benefits to the Level 2 MK 1919 are the pistol grip, safety, and magazine controls. The manual of arms is very similar to the AR, and the use of AR-style magazine release and insertion will keep this gun reloading faster than a Saiga-12 with rock-and-lock magazines.
Level 3: Similar modifications to a nice AR. Expect adjustable stocks and enhanced grips. Ambi controls may also be a possibility. I'm not as familiar with this level of MK 1919, and the action shotgun gunsmiths will have the best knowledge of what you can get, and price point. I'll say that if I was going this route, I'd get the gun worked over, and then send it to a Remington 1100 specialist, just to be sure.
I have not held a MK 1919, but reviews indicate that it is both lightweight and controllable. The barrel/buttstock geometry is all AR, which will serve to minimize muzzle movement and recoil. The Saiga-12 isn't overly heavy, but I do not consider the Saiga-12 lightweight. Additionally, the AK barrel/buttstock geometry has inferior controllability under recoil. Practice minimizes these differences, but they will always be there. As an aside, I once had the opportunity to handle, but not fire, a USAS-12. While I was in complete gun nirvana holding it, the USAS-12 is a total pig, and gun weight may prove an important factor.
I got my Saiga way before the MK 1919 was available, and I'm somewhere between Level 2 and 3 with it. It's my favorite gun. If I wanted an AR shotgun (and I do, wow, do I), my preference would be for the 20 gauge CMMG design that seemed to be much more of an AR in action design. The Remington 1100 action will get the job done, but I would not care to switch into one from an AK action. However, if I were back at my original level of knowledge and experience back at that gun show and seen a MK 1919 for the same price as a Saiga-12, I know that I would have been on that gun like white on rice, and had a very happy time with it.
You mention an interest in a rifled barrel, and I am not aware of either gun being offered with a rifled barrel. Saiga-12s have been imported in unchoked, fixed choke, and threaded choke variations. I do not know if the Saiga-12 factory threaded chokes offer a rifled choke option, but a Saiga-12 modified to accept aftermarket chokes would give you that rifled choke option. I understand that the MK 1919 has threaded choke tubes, but I do not know if rifled chokes are available.