If you're being offered these for the same price then, on the face of it, the X10 should be the winner. It's a more expensive, higher spec phone with faster processor, bigger and higher res screen, bigger memory, bigger everything in fact! It's got a higher spec camera with lots of extras and should have a better music player (I say this as I have the Desire, and the music player on that is very basic).
That said, the Wildfire is the so-called budget version of the Desire and runs a later version of Android than the X10 (although I've no idea how important that is). I can't fault my Desire (music player apart) and much prefer it to the X10. If the Wildfire is as good as the reviews say then you have an interesting choice. It may boil down to how big a phone you want to carry around, or whether you're loyal to a specific brand. Also, how important to you are the camera, music player etc?
If I'd been in your position before I got the Desire then I'd have got the X10 straight away. Now, I'm not so sure!