Points:
1) All cables must be CAT6 and the modem/router, and network chip/card must also be gigabit compatible or you'll be bottlenecked by whatever cable/component is too slow.
2) CAT6 is pointless for network in most countries.
*My ethernet connection is 725KB/second which is LESS than 1MB/second. Cat5 can handle over 10MB/second. Cat6 can handle over 100MB/second in theory but in reality your network will throttle you.
So unless you have an awesome network connection that's far above average it's just pointless. The only OTHER usage of CAT6 is for LOCAL networks in your house for file-sharing and that definitely WILL make a difference.
For example, if I shared files between two computers (hard drives) I might average 70MB/second which is far above CAT5 speeds. I would require THIS setup:
1) CAT6 cable from PC#1 (gigabit capable network chip) to router
2) Router (must be Gigabit capable)
3) CAT6 cable from router to PC#2 (gigabit capable network chip)
In the above example, we require BOTH network chips to be gigabit capable, the Router to be gigabit capable, and CAT6 cables between both PC's and the router.