My recommendation would be for you to get the Nexus One. Though the Nexus One and the Desire both have the same 1Ghz Snapdragon processor, the Nexus One now runs Android 2.2 "Froyo" that has a JIT compiler that can execute code up to 6x as fast as the Android 2.1 on the Desire. The fact that the Nexus One is the official Google phone means that it's going to be the first to receive the latest software, while other devices (like the Desire) will lag behind or not get updated at all.
The other big deciding factor is HTC's Sense. Though many people like Sense, there are others, including myself, that prefer the stock Android UI. If you can, try and see if you can play with both UIs before deciding which one you want to buy (stock Android 2.1, which can be found on the Motorola Milestone, is similar to stock 2.2, but lacks a shortcut to the phone dialer at the bottom on the home screen).