Only just started checking the game out, but at first brush it's about what I expected -- performance is pretty similar to BF4, at least so far. I started out by copying my BF4 settings:
Most settings are on High, except for Medium Shadows, Post-Processing Effects, and Tesselation. I disabled AO. AA solution is Medium Post-Processing AA.
System is:
i7 860 (at 3.3ghz)
GTX 570 (1.2GB VRAM, very minor O/C that I can't remember

)
8GB system RAM
Win7
Slightly cheating on resolution, being back on a 1680x1050 screen until I replace my dead 1080.
The benchmark gave me 56 average FPS, with a minimum of 43. In the very starting area of the actual game, running down the path is mostly 65-75 with some 80s. I broke 100 going up the stairs, but that doesn't really count for anything. I dropped to the mid 50s when passing some fire and when encountering the group fight.
Just for fun, I tried enabling SSAO and 4x MSAA while disabling post AA, and the benchmark ran at 37 average, 29 minimum. That's too low for my personal tastes, but people who don't mind 30 FPS can apparently get away with fairly aggressive settings even on old hardware with this game.
I expect to see a framerate hit when I get into more open areas, but so far it looks and runs great. Yay Frostbite.