The latest Fedora release is Fedora 8. The latest Ubuntu release is Ubuntu 7.10. They can both run on AMD machines.
I always recommend new users to try several Linux distributions to learn how each does things differently. So, I'd recommend you choose either one of the two first and then when you've become quite comfortable with it, switch to the other.
Graphically, you'll find Fedora and Ubuntu to be quite similar. Most of the applications that are available for Ubuntu are also available for Fedora. But there are some applications that are unique to each.
It's really a matter of choice what distribution to use. I suggest you give them both a shot and decide which you like more.
Cheers!
Coauthor of Beginning Fedora: From Novice to Professional published by Apress.
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