Either one will do what you want and it's really a toss up. On average, one isnt better than the other. Both companies make rifles that shoot and rifles that dont, both make rifles with mechanical problems/defects and rifles that dont. That's just the way mass manufacturing and quality control work these days. Things man made can, do and will break, quality can slip through the cracks, Remington and Savage are not immune to this....it happens.
I suggest to get your hands on the models that you are interested in and handle them, compare them side by side if you can. Both will most likely have some things you like and dislike between them. Feel the weight, the balance, the way the bolt cycles, fit and finish, the stock in general as well as the forearm stiffness, the Savage might have a free floated barrel while the Remington doesnt. What bullets are you planning on shooting relates to what barrel twist might suite your needs better will a 1:10 or 1:12 do better, does it even matter to me??......and on and on.
We are all different and have preferences, some like cream with their coffee and some dont. There are going to be Savage fan boys as well as Remington, Winchester etc etc. I have been shooting a long time and am blessed to have a good selection of firearms, more than a man should have. I get to run firearms side by side and compare apples to apples, that's where my opinion comes from. I have 5 different different 308 win rifles I shoot on a regular basis. Each one is it's own person if you know what I mean. One day a Remington might turn in the best results while Savage will on another outing. My personal Rem 700 308 shot exceptional out of the box with various loads while my Savage 10FP drove me crazy and took a looooong time to find a load that it liked. Is the Remington better than the Savage? My honest answer is no. They both perform and do what I ask of them.
It comes down to what you feel is best for you and your budget. Again, firearms in general can be a personal, please have an open mind and decide on what you think. If you have questions, do some homework, look at the gun companies web sites, get your hands on them etc.
Of course you could do what I did and get several makes of 308's and run em side by side and come to your actual "hands on" conclusion