The only reason to use Cat6 is if you think you'll one day get 10 gig ethernet over copper at home. The standard has been out for years (something like 15 years) but it's basically not got adopted, so no equipment includes this. Anything that does run 10 gig is typically over SFP+ connectors, which are optical based for any length > 5m, and although it's a great standard, go check out the prices of SFP+ switches and you'll see that it's aimed squarely at datacentres, and there is no real home market for this stuff.
So i'd say go with Cat5e, the cable is cheaper, and thinner so easier to install. Saying that, if you do go with Cat6 there is no downside once you've paid and installed it, since it's compatible with everything Cat5e covers, it's just I think it's a waste of time as I stick with what I know.