Re: The better rifle?
The .338 LM would be a great caliber for long range hunting. However, if you are going to be packing a rifle on your back while hunting, you may prefer something like a Tikka T3 in 300 WSM or 300 WM.
If you are set on a .338 LM, I would consider the Savage 110 FCP HS over the ones you have listed. It is nearly half the price of a TRG 42 and will be a fine rifle to get you into long range shooting/hunting.
While some will tell you to bypass the Savage and go straight to the Sako. If you were looking at the Sako, some would say forget the Sako and go straight to the AI.
I personally went with a DTA SRS so I could shoot multiple calibers out of the same platform. I have been very happy with it and would recommend it to you if you were looking for a rifle in that price range.
All of the tactical Savage rifles that I have shot have been tack drivers. If my price range was $1,500 for a .338, I would not hesitate to go with the Savage 110 FCP HS in .338 LM.
Best of luck with your decision.