You'll find with the Wildfire that you are more restricted due to the smaller screen and some apps won't be available in the market. If you're into small phones, the Wildfire is definitely sexy, but it won't be able to prove the full Android experience, IMHO.
i havent had the desire, but ive worked with the wildfire, the wildfire is alright.. a good entry level android and really smartphone altogether.. i think it runs android 2.1 if im not mistaken, not interested in seeing what it really is right now.. but trust me, its by no means fun once u get to know it... when u first start you say "this is great!" then when u get to know it better... u want the full experience.. its like a teaser of android really... and a teaser of HTC altogether..
The Wildfire's screen (at least the old one) is quite pixelated. I've seen many people regret getting one because of that. As others have said, the size is limiting. You can't get a decent keyboard, for instance.
I had the Desire, then upgraded to the Desire HD. I loved them both. My DHD just broke, so I will probably move onward and upward.
If you are just going to use the phone as it is, then Wildfire S is not a bad deal.
However, Desire is still more capable even though it is much older device. It is even much more fun to use when rooted and flashed with custom ROMs.
Desire would be definitely my choice.