If you're upgrading within the next month or so then the new nexus won't be on sale yet. Goes on sale in early December usually.
So I'd say Galaxy S3 or HTC one X or S. All three are superb.
I wouldn't touch the galaxy nexus as it's hardware is old now. Hardware wise is is inferior in every single way to the S3, Samsung the galaxy nexus is a modified galaxy S2.
So your choices are with Samsung or HTC and the differences are as follows. The One X is nicer to hold and look at but has no removable sd card slot and the battery life is below average. The one s is a smaller screened version of the one X but has better batterylife due to its S4 processor.
The S3 is the best phone on the market and that's why it's selling in the multi millions. Some people don't like the weight, and design or the plastic chassis. But aside from that the phone is faultless.
Most on here are android veterans and love having the nexus phones because they get vanilla android and get the new updates a couple of months before everyone else. But since you've been on a Desire for two years I can't imagine you'll be too worried about timing of updates.
My opinion on the matter is this, HTC and Samsung take Google Android and improve it by adding their own features and enhancements, so there is a little wait after each release of android before they layer their enhancements and release to their phones.
If you want a single recommendation from me, and go get the Galaxy S3 it is simply the best phone you can by bar none, it has the best hardware and it has the most features and that's why you should get it.
Truly stunning phone.
Cheers Conor......
I like the HTC skin on my Desire but the battery life is scandalous and by all accounts they haven't sorted this for the One.
The S3 looks lovely but I like to try and do something a bit different rather than plum for the thing every other bugger has. (and no - I have no interest in a Windows phone)
I thought the Nexus could be fun but I will can't be arsed with rooting and custom roms etc. I just want a decent skin atop a quality piece of hardware........