well, between ubuntu and fedora i would say ubuntu.. it's a very nice distro, but i've never used it on 64...
I would actually probably recommend SuSE because they were the first to offer 64-bit Linux, and with the corporate backing of Novell, I'm confident it will probably have less bugs...
Give SuSE a shot.. it's a little bloated..but no more so than Fedora..
Try a few different ones and see what you like better... I started Linux with Red Hat and then Fedora.. and now I can't even use it... I like the more manual distributions...
Good Luck though..