However Crysis 2 did have some
Frame-rate (FPS) issues.
Will Crysis 3 overcome these problems to claim the best looking game on console and PC for this generation?
Best-looking =/= frame rate issues fixed.
It will certainly be the best looking game on consoles and PC, however I don't know how smoothly it will run on consoles. On PC's you can do stuff like cut resolution/settings (along with console commands), or upgrade to a more powerful GPU setup to to get the game running smoother...but with consoles Crytek pretty much have full control over how the game runs and looks any given moment.