Cat6 cable has much better protections against electromagnetic inteference and signal reflection/crosstalk. It really doesn't have to do with the number of pairs or materials used in the wire, but how well and how far the cable can transmit data without interference.
Because of the more twists and better shielding, can6 is rated at 1gigabits per-seconds, at 100 meters in length. But if you shorten the length I think you can get up to like 10 gigabits per second (not that any one has a nic the can go that fast).
And Cat5 is 100megabits per-second at 100 meter but you can get it up to 1 gig when shorten.
So if you are running short distances, you really shouldn't notice a difference, between the two.