Well the differences are as follows:
Screen: Samsung has 4.0" Super AMOLED, Desire has 3.6" AMOLED, possibly soon to be S-LCD
CPU: Samsung has 1Ghz Hummingbird CPU and PowerVR GPU, Desire has 1Ghz Snapdragon CPU and no dedicated GPU
RAM: Bout the same
SD: Galaxy has 8/16GB in built internal memory and a slot, Desire doesnt have built in card but has a slot
Build: Galaxy apes the iPhone from the front, is very light, doesn't feel too flimsy and is very thin for a smartphone BUT is totally plastic. Desire has a nice rubberised metal case and its own style and is frankly the better of the two appearance wise
Camera: Desire has a flash and 5 Mpixel, Galaxy has no flash and 5 Mpixel, but its pretty good in low light for me.
OS: Galaxy has Android 2.1 with Samsung TouchWiz 3.0, Desire has Android 2.1 with HTC Sense, both can be modified as you wish and both are due a Froyo 2.2 update, the Desire will probably get it first.
Battery Life: Both will probably give you around a day of usage (i.e. WiFi on for some of it, GPS on), maybe 2 if you arn't a "fiddler". I have been re-charging my Galaxy overnight though.
Multi-touch: The Galaxy's multitouch hardware is definately better than the Desires, though for the very vague usage it currently gets in Android (pinch to zoom) it's hard to notice.
Other things of note: the Desire has a nice optical trackpad, the Galaxy doesn't.
Really though, both are very fast, both are very pleasant to use and both have their merits. I *think* the Desire still pips it for me just because its build quality is better and it has a flash, but I have a Galaxy S purely cos Orange (who i'm with) havent had stock for weeks, and still don't!
I'm very happy with the Samsung, but either are great phones.
ultimately, if you can, go and have a play.
EDIT: Forgot to say, as both have Android, really both have the same basic functionality. They can both tether afaik, both have the same Android camera software, which is very comprehensive, data/email and web is what Android was born to do, audio and mp3 playback, again no worries and there are literaly thousands of games, free and not, on the market. Though in theory the Galaxy may be superior here for well written 3D stuff due to its hardware GPU.