CAT6 is higher rated speed-wise than CAT5e. However, both are fine for Gigabit Ethernet.
I'm a n00b, but after dealing with some CAT6, I decided to run CAT5e everywhere. Why?
1) CAT5e can be a lot cheaper.
2) CAT5e connectors (jacks & plugs) are usually a lot cheaper.
3) CAT5e cable (and jacks) are a lot easier to find locally, especially if you have colour preferences. With CAT6, it's around, but specific types are harder to find.
4) CAT5e is generally thinner - less loops in the cable - so it's easier to work with. Plus there is no 23 AWG CAT5e AFAIK, so pretty much any RJ45 jacks will fit. (Some CAT6 is 23 AWG.)
5) I get just under 900 Mbps with my runs of CAT5e cable. With CAT6, I also get just under 900 Mbps. (BTW, I had some existing CAT5 100 MHz cable, and I got close to 900 Mbps over that too.)
I'm not future-proofed for 10 Gigabit networks, but quite frankly, I don't care. Plus, for 10 GigE, you'd probably want CAT6a cable anyway.