What are the advantages of each? Are there any pro or cons to each one? Thanks

Simple break down:

Recoil:
Lighter weapon by design
More preceived recoil
Can be round sensitive
Changing the weight of the weapon can cause failures. ie added optics

Piston:
Generally heavier
Less preceived recoil

Is there a difference in Recoil and inertia operated?  basically the same thing right?  Anyways I can not use Benellis because the catch my cheek bone when during recoil.  Pump Guns, Single Shots, Doubles and Gas Operated I dont have a problem but every Benelli auto I have shot catches me right in the cheek bone and hurts like a SOB.  Sucks to because I can run a pretty good time with an M1 in 3 gun comp but it aint worth the pain for bragging right shoots.  So I stick to the 1100.

Recoil and inertia are different.

Recoil operation is where the breech and barrel are locked together and travel rearward before unlocking.
Long recoil (ie A-5) is where they stay locked together for a distance greater than the length of an unfired cartridge.
Short recoil is anything less than this. (ie M2)

Inertia/recoil guns are great because there is no gas system to clean. They do tend to be a bit sore on the shoulder after a few rounds.

Recoil operated guns (most notably the Benelli inertia system) are extremely reliable, while some claim that gas operated guns have less recoil, but I have never been able to tell the difference in recoil between the two.

The Benelli doesnt hit my shoulder any harder at all, it whacks me in the cheek bone.

Gas operated guns are only percieved to have less recoil because of the cycling of the gun fooling you into thinking the recoil has been spread out over a longer period of time.

Actually at the moment the gun fires The bolt is locked into the barrel extension and every bit of the recoil is transmitted into the reciever through the stock and into you shoulder. It is the same impulse you would get from a solid locked break-open shotgun. By the time that bolt unlocks that shot or slug is long gone from the barrel and the initial recoil impulse has passed.

The only reason they may exhibit less "free recoil" is the added weight of the gas operated semi auto mechanism.

Quoted: The Benelli doesnt hit my shoulder any harder at all, it whacks me in the cheek bone.

I get the same thing from many shotguns too. I even get it really bad from my AK.

Quoted: The Benelli doesnt hit my shoulder any harder at all, it whacks me in the cheek bone.

Sounds like the Benelli M2 with the redesigned stock would be great for you.