The N1 has standard Android (some people prefer this), easily rootable, more ROM choices available if you're into those, noise cancelling microphone, slightly better talk time.
The Desire has slightly more memory, the four buttons (home, back, call, end call) at the bottom of the phone are physical (most people prefer these), and it has an optical trackball (having experienced both, I prefer this). It also has Sense UI (some people prefer this), but unfortunately, in *released* versions of the Desire you can't drop back to standard Android, as the Home application is not installed, and can't be without rooting. It also has Bluetooth 2.1 (as opposed to 2.0). Desire has better standby time, and an FM Radio.
If I had to choose between the two, I'd get the Desire.
Depends where you are. If you're in the US you probably want the Nexus, if you're in Europe or the UK you probably want the Desire.
Also there's the question of where you are going to use the phone, EU or US? 3G band support on the N1 is slightly better suited to the US, and on the Desire it's slightly better suited to EU/UK, but it depends on the mobile network.