Expanding what I said before - the UK Hero uses 3G (in the form of UMTS) on frequencies 900 & 2100. Networks in the US don't use this, they use 850, 1700 & 1900. These are like radio stations, you need to be tuned in exactly and the UK Hero simply isn't in the US. To the best of my understanding, you will get 2G (so calls and texts are fine), probably EDGE, and Wifi and Bluetooth.
UMTS frequency bands - Wikipedia, the free encyclopedia
Jason Bourne's phone was probably also limited to 2G, although there are phones out there which give 3G on both sides of the Atlantic. The Samsung i7500 Galaxy, due out any day now in the UK, for example. That might be a better choice for you.
Incidentally, Orange won't sell the Hero to PAYG (pay as you go) customers, so you'll need to get an unlocked one. I just bought a Hero from Expansys, they've been good in the past. No idea who will have the Galaxy, or when it will be out.