Differance between hardball and wad cutter

What exactly is the physical difference between a hardball and wad cutter gun and there use in competition? And why would I want one over the other?

A hardball gun is defined by the CMP for EIC competition. It lacks certain features like a beavertail safety, or bobbed hammers, it must have a 4lb trigger and in matches (thus far) you need to shoot a 230gr FMJ. A wadcutter gun does not need to meet the restrictions, can use optics, and needs a trigger of 3.5lbs, etc etc. See the NRA rulebook. 

CMP rules for hardball gun are in Rule 6.4 page 33 of the 2014-2015 rulebook.

I wouldn't even worry about it right now, with the proposed changes coming 1-1-15 there may very well be no difference. So just wait and see what they do.

I think the iron sights requirement will remain in CMP matches.

But I also suspect that all of us will be surprised at at least one thing in the final package they announce. It would be kinda fair for everyone to be wrong about at least one thing...