I have no knowledge of the Browning, I do of the Savage.
What caliber are we talking about?
Savage is some and some, though all mine are Savage as I can and have modified each one.
First the Savage action is up there with solid or more so than anyone. Its an old design and its heavy, solid, good bolt and lock up. Equal to the best in that regard.
Magazines and feed have been an issue, I don't care, but I shoot single shot off the bench anyway. It is a factor, may require a bit of work.
You can't beat the acu trigger short of a $100+ after market trigger.
Savage Varmint types get you two big advantage, the heavy Varmint barrel and the Varmint version of the acu trigger that goes down to 1.5 lb set.
The best bargain out there is Cabell Only Savage 12FV that is often on sale for as low as $300 (Cabella's has rebates, Savage has them and you can combine them at times) .
I suspect a Browning will last several life times, if you want to change things, then the Savage is vastly better and it will last as long.
My most modified one has a 7.5 Swiss Loather Walther barrel, was converted bottom bolt release to top bolt release and sits in a Boyd's Thumb hole blind mag hole stock (with a filter block for a true single shot)