Minecraft is CPU intensive due to the nature of the game and possibly poor coding, Java can be just as fast as the alternatives.
It doesn't require a hefty video card, but onboard processor video might still be a bottleneck. Even upgrading from a 570 to a 770 saw a decent bump in performance on one of my computers (that had a i7 processor so probably wasn't CPU bottlenecked).
EDIT: There's a bunch of benchmarks here:
http://minecraft.gamepedia.com/Hardware_performance