I like the concept of the DTA but I'm just not a fan. I'm short with short arms and the bolt was awkward for me so I can't imagine shooting it as a taller person. I didn't notice any problems with the mags but once again they were awkward to use, I much prefer a mag well out in front of the trigger by far. As I said in another thread, beyond the fact that the gun just doesn't fit me well, having my face at the chamber of a 338 scares me a bit. In the event of a kaboom (it would be rare and would likely be a reloading mistake, or faulty ammo) you would be very fucked up. You're going to bleed most likely with a traditional style rifle, but I'm much more comfortable with that foot between my face and the chamber. It's a cool gun and it seemed to be great quality but its not my thing. If I win the lottery I'd probably buy a Covert just because, but otherwise I'd never buy one.
I had a AWSM and it was a great gun, definitely the standard by which others are judged. I would certainly put the AI at the top of the food chain. I haven't shot an AX yet so I can't but I just picked up my 308 so that is going to change. So far I like the stock though which is the only major difference between the AWSM and AX. The AX got a few other upgrades as well like a double stack mag for the 338.
I shot a Barrett 98B and handled a MRAD and really liked them. The 98B was a 1/2 MOA gun no problem great quality. It's not a battle proven gun like the AI but it is still a great gun and I wouldn't hesitate to buy one. My only complaint I could find was that the forend was a bit short, I'd like to see it just a touch longer to get the bipod out a little further, but it wasn't the end of the world, merely a suggestion I would make. If it was me though, I'd buy the 98B over the MRAD. The only real advantage to the MRAD is the barrel change which is vaporwear at this point, and you're wanting a 338, not a one gun deal. A folding stock on a 338 is a moot point for me because its already so long that folding away 6-7" isn't going to do much for you. The 27" barrel model will fit in a standard 51" drag bag as is and a folder with a can won't get you in that bag so I don't see the point.
All around I would have to say the new "bang for the buck" 338 is the 98B. For just over $4K you get the rifle with a swiveling Harris bipod, two mags, and a Pelican case. I know you're not looking for ultimate value here obviously, but I just figured I'd point out what a good deal the 98B is. For the price of the MRAD though I don't see any reason not to pony up the extra cash and get AI, it's a superior rifle and battle proven. The 98B and AI is worth debating about though, there's enough of a difference there to wonder if you really need to spend the extra but once you spend the extra $1500 for the MRAD the AI isn't much more of a jump.