Update:
I loaded up a new Minecraft world with all video settings at maximum and ran around for a while.
Was getting an average of 140FPS with dips to 70FPS and highs of 240FPS. I got periodic STUTTER due to texture loads which I assume everyone gets (not when I stop running).
*When I tabbed out and looked at my CPU usage I calculated a dual-core modern Intel would have enough processing power for my tasks.
I can't speak to MODDED usage but I suspect that's more of a VIDEO load and the CPU impact would be minor.
My FRAME RATE is tied mostly to the graphics card. I normally use VSYNC so I get a solid 60FPS, thus a GTX680/770 is generally overkill though I can't speak for mods or perhaps different maps.
My system:
i7-3770K@4.1GHz
GTX680 @1200MHz