The model 25 is heavy, the "lightweight"

varmint models are a pound heavier than the model 10 Predator. They also don't use a barrel nut the way the 10/110 style actions do which is a major downfall in my opinion.
If you are going to build a full blown BR rig you probably aren't going to use a Savage action, but you probably aren't going to use a Remington action either considering the available aftermarket options. Savage rifles/actions have done very well in all but the highest levels of BR competition and Savage's F and F/TR rifles have made an impressive showing lately against many custom built rifles.
Savage rifles are also great if you are a DIY kind of guy. Bolt heads are easily changed and barrel swaps are only a few dollars worth of tools away. Pre-fit Savage barrels are becoming more and more readily available and affordable. I've got nothing against Remington and own several but would be hard pressed to buy another now that I know what
I can do with a Savage.
The model 11 or Stevens 200 would make a nice lightweight calling rifle. I don't like the factory synthetic stock(they work I just don't like the feel) but with a little work and some spray paint you could have a very affordable and functional rifle.
For what it's worth the advertised difference in weight between the Remington Model 7 Predator and the Savage Model 10 Predator is 1/4 pound.