I've worked with dev builds of this project on both major platforms, Windows XP Home, XP MCE, Vista, Win 7, as well as Ubuntu, Kubuntu, Xubuntu, and even ReactOS*. In a nutshell, it is most stable on whatever OS you're most familiar with and can tweak the easiest.
Most (but not all) bugs that I've seen are the same across platforms, although some do affect only one operating system.
I've also noticed that on some machines the game runs faster or slower depending on what you're running it on, sometimes on Windows it is faster, other times Linux. I haven't found any pattern to this yet, however, or figured out what the key factor is that makes that difference.
*ReactOS isn't really from either family of operating systems, and I wouldn't recommend attempting to run UFO:AI on ReactOS at present unless you really know what you are doing (and don't mind breaking things).
Edit: Looking at the specs you posted, I'd guess it would run OK on either operating system on your machine.
