Cat5E and Cat6 are cable standards. 100Mb & 1000Mb Ethernet are networking standards. Running 10/100/1000Mb Ethernet over Cat5E or Cat6 gives you a length limit of 100m.
Cat6 needs a lot more care when installing than Cat5E, e.g. crimping, twisting, bend radii and termination, and all your modules/patch panels need to be Cat6 too.
One very important point is if you haven't tested your installation using a proper Cat5E/Cat6 tester, as apposed to a modtap tester, then it hasn't actually been proven at either standard. Yes, it might work, but not to it's best ability or for your future needs.
Would I install Cat6 for a new build? Not sure really: as Gb is really over kill at home anyway, a nice to have obviously, and that is no problem with Cat5E. If it was only 10-15% extra cost then probably.
Kris.