I've had an ATR in .30-06 for over two years. It shoots very well with Rem Core Locts; Winchester Power Points and Federal Power Shoks and Hi Shoks, all with 180 gr rounds. Overall, I'm impressed with the rifle. Nothing I've shot has grouped larger than 1 1/2" and most, especially the Federals, will shoot 1" quite reguarly. I'm impressed enough with mine that I bought a .308 wood stocked version last fall and plan to buy one in .270 with the Marinecote finish in the near future. I first mounted a Wal Mart Tasco 3X9 but last summer switched to a Bushnell Legend 3X9X50. The ATR in .30-06, a Bushnell Legend and Federal Power Shoks, a exellent combination!
Regarding the Stevens, I only have one in a .22-250, but don't have much range time with it. I installed the Tasco from the ATR just to see how it would shoot. So far it seems that it will be a shooter. It does have a heavy trigger, but I'm not really bothered by that. The edges of the"checkering" is sharp and its easy to jab yourself if your not aware. I have read over on the Savage Shooters forum that the Stevens stock does tend to flex a bit more than the Savage black stocks and some have changed to them.
Something else you may want to consider is an older Savage mod 110 w/o the accu-trigger. They became the Stevens 200. I picked one up last year that had a wood stock in real good condition for $230 at a pawn shop with a Simmons 3X9X32 scope. Since after the holidays, I've seen a bunch of them at gun shows and shops. Mine shoots as well as the ATR.
Search back a few pages for other info on the ATR. There are a few members here that own them and like them very much.
The Savage/Stevens has a proven history to draw from whereas Mossberg has a reputation for introducing a decent rifle only to discontinue it after a short run. If your really interested in the ATR, do a Google search for the Charter 2000 rifle. This was the forerunner to the ATR. Mossberg bought the rights to produce it, made some minor changes, then introduced it as the ATR. The Charter rifle recieved some very good reviews regarding construction and accuracy.
You probably wouldn't go wrong with either. Once you finish your research and handle them, it would pretty much be personal preference.
Hope this helps.