Looking for one 50 BMG rifle.  I’d love an M82 but can’t justify the cost.  Primary use will be from prone or a bench on a nearby 900 yard range.  I have access to a 2000 yard range a few times a year several hours away.

Any recommendations on one over the other?

I wouldn't buy either one.
For the price of an M99, you can buy a Serbu BFG and a lot of ammo.

Both will hold MOA or better with quality ammo and the BFG will be a little behind them.

Just going to come down to personal preference, which one you like over the other...

I have an M82A1... really fun gun but I'm lucky to get 1 MOA out of it.  Especially with surplus ball ammo.  Also, the trigger is one of the worst I've used.  

Sounds like your real decision is bolt action vs. semi auto.  I was looking for a bolt action 300 WM and somehow ended up with an M82A1.  What an impulse buy that was...  They were cheaper when I bought mine, I think I paid a hair under $7 and I already had a scope I was going to use on it.  I wasn't looking to spend that at the time but you only live once and to this day I'm still glad I got it.  

There's nothing that tops a semi-auto 50 BMG!  The Serbu version is a great gun as well but those are nearly impossible to find.

I'm partial to the AR50. With barret being bought by aussies, that's concerning for future service.

I've heard the M99 has the same trigger as the M82... not sure if that's true, but if so the AR50 would easier IMHO to shoot accurately at distance.

No. The 99 trigger is not the same.  The 82a1 style rifles lift a transfer bar that in turns lifts the sear out of the way of the firing pin extension very similar to the M2 machine gun.
The 99 has a connecting rod the pulls the sear off the engagement of the cocking piece similar to normal bolt action rifles.

I love my 99 and think it's one of the best do it all 50's out there. For exclusive target work from prone and bench it's going to be pretty hard to beat an AR50. For most people either will work fine.

My take. Probably forgetting a bunch.

AR50
Pros
Conventional layout
Better Trigger
Less recoil (partly due to brake partly due to weight)
Cons
Long as hell. Cases and bags are specialized therefore more expensive and harder to find at times
Heavy (depends on usage obviously)
You'll have to figure out a bipod or support if you want one (Current website mentions GGG Bipod so maybe they come with one now even though it's not pictured)

Barrett 99
Pros
Compact enough to fit in normal cases
Built in rail cant( Can't remember if the Armalite does or not)
Comes with Bipod
Cons
Trigger takes a bit to get used to. It will never be a nice bolt action trigger.

AR-50 owner here.  Heavy, accurate, lower recoil better price and a bit easier to find.  If you go for the AR50, get an APA bipod if you can.  It does add some weight and $ but your rifle won't roll over and crush your expensive optic like can happen with a Harris type bipod. I recently got a soft case for mine that fit just fine for around $100 on Ebay.

Having shot both, I bought the AR50. The barrett is nice, but the AR50 has a better trigger, less recoil, and was a little more accurate with identical ammo (may have been the trigger). The Barrett is more handy, but not worth the trade offs to me.