I have both a Browning A-bolt Stainless Stalker in 338 WM (from 16 or so years ago), and a Remington SPS blued (black) in 243 Win (from this year). So here's my take on the two:
The Browning has a recoil pad that I'm almost certain was fashioned from granite and painted black. Maybe they've improved them since? I don't know. The Rem has a limbsaver - a very good recoil pad.
The Browning is one of the most accurate rifles I own. So is the Rem.
The stocks on both are....plastic and cheap...and very functional. If I had to give a nod to one here, I'd say the Browning is a bit less slick and a bit less cheap-feeling compared to the Rem.
The Browning, when on safe, locks the bolt, you can't open it on while on safe. With the Rem, you can open the bolt on safe. I never really liked that feature of being able to open the bolt on safe (getting it opened by brush, etc), I guess only because I'm used to the 3-position mod 70 safety. Your preferences may differ.
Both actions are slick, although the Rem is slicker. If a 60-degree bolt throw on the 3-lug A-bolt vs a 90-degree bolt throw on the 2-lug Rem makes a difference for you, there's a factor to consider. It hasn't been a factor for me.
I kept both factory triggers. Never adjusted the Browning, and it's fine around 3 pounds. I adjusted the Rem down to around 3 pounds. A friend who has the same Rem (which is also very accurate) replaced his trigger with a Timney.
I haven't heard of a solid complaint personally (excepting internet chatter) about either rifle.
I'll say this: I have heard that various gunsmiths can effectively accurize Kimber blued rifles, but hesitate to take on accurizing the same Kimber model stainless rifles. I don't really know if that's a materials issue, or a manufacturer-specific production issue. SS is more difficult to machine than chrome-moly, and I can envision manufacuturer's trying to eke out more rifles on dull tools with SS than CM, and thus getting poorer quality with SS.
Tough choices....I'd suggest you get both and report back to us!