I have the Savage Model 12 LRP in 260 Rem. It is a heavy target rifle (14.2 pounds with 6X24 scope) and is very accurate as you would expect. While the 260 Rem itself is great, that rifle in particular would not be my first recommendation for a deer rifle as most people would find it too barrel heavy with the no taper target barrel. (It is however pretty nice with a varmit contour 270 WSM barrel - but that is another story).
I use my LRP mainly as my long range (500 yards and out) prairie dog gun. It just hammers them with the 95 gr VMAX. It is not that I would not take it deer hunting and I have loads worked up in case I want to do that. I have used those loads shooting from field positions (prone off dirt) just to see if it would work long range for deer and went 4 for 4 on a playing card from 500 yards. However, I've got better balanced choices - for example a custom 7mm WSM
based on a Savage model 12 FV which weighs only 12.5 pounds.
As to Savage versus Remington in general, I'll take the Savage every day. I have 4 of them and they all shoot great and I love that you can swap barrels, bolt heads and/or magazines to create whatever you want in about 15 minutes - not to mention the Accutrigger, 3-position safety, etc. etc. My latest Savage I got a few weeks ago is a model 12 VLP DBM in 223 Rem. Right out of the box with no barrel break in or any mods, it put 3 into 0.344" at 200 yards. The LRP has done similar. All the Savages seem to shoot pretty good right out of the box with whatever ammo you feed them but if you do a little load development the groups get tight.
Last but not least, my nephew has a rather heavy full custom 260 Rem and shot three deer with it last year. They ranged from 500 to 600 yards and he shot all three of them in the head (yes, on purpose). Needless to say, for him the 260 Rem is working well for deer. Good luck with whatever you pick.