For the most part, no. In some cases, it could be slower, but usually it's not that bad of a hit when compared to XP (maybe around 5%). In most cases, it's the same as Vista and in some cases, is better than Vista (again, maybe around 5%).
Mind you, these are figures I've read in gaming magazines, etc. If the games are running fine in XP, then there really is no need to upgrade to Vista or Windows 7 unless you really want DirectX 11 support and access to all the great tweaks that Microsoft did to the Windows 7 UI. Oh, and of course, XP is on the way out, so that is another reason.
XP runs faster, but the difference is negligible. In most cases, you might lose up to 5 framerates, so depending on your machine, that could be a bad decrease or not make a difference at all.
For example, if you're getting 35 fps in XP, then you might drop to 30. For some, that's fine. For others, it not. What it really points to is, you need to upgrade your machine anyways, especially if you want to play the latest games.