AI is back in business.
Here's the order I'd buy them in:
1. AI ASM338
2. SAKO TRG-42
3. AR-30
I've shot the TRG-42. I've shot an AWM300 (the 300WM version of the AI), and I've handled the AR-30. The AR-30 is the cheapest of the bunch by a long shot, but shoots good.
The TRG and the ASM are really top of the line, nothing really better. They are comparable, but I would choose the AI just because it seems tougher and more fieldworthy. The TRG-42 has a chrome-lined bore.
Barrel replacement is done at the user-level with the AI. I don't think that's true with the TRG, and it's definitely not true for the AR-30.
-z
ETA: For any of these, you really need a good scope to take advantage of the ballistics of 338. I'd say to start looking at the Nightforce 5.5-22 or a Leupold MKIV M1 and go up to a USO from there, if you can afford it.
Also consider the cost of shooting. Factory ammo is about $4 per round. Brass is expensive. It's basically the same cost to reload as 50BMG.