Do a Search of the Private Flying forum, where this gets raised quite regularly - mainly in repsonse to people considering training for a JAR PPL in the US.
I won't even try to answer completely, because I'll miss things, but I'll get things started:
Airspace
In the UK, the open FIR is class G - no clearance required for VFR or IFR flight. There are radar services available in much of this airspace, but no requirement to use them, and no guarantee that they can separate you from other traffic.
In the US, the open airspace is mainly class E, so a clearance is required for IFR flights, and you will be separated from other IFR flights.
This is the biggest practical difference. Apart from this, control zones in the UK are generally class D, regardless of the size of the airport (a few exception, mainly Heathrow), and there are many controlled airfields which are actually outside of controlled airspace. In the US, control zones will be class B, C or D depending on the size of the field. In practice, though, this doesn't make much difference except for the type of separation you can expect. There is no such concept as a controlled airfield in uncontrolled airspace in the US.
Communications
When receiving a control service, there's very little difference. Americans tend to be less formal - the only area they are very strict on is reading back runway hold-short instructions. In the UK, there are lots of things which you need to remember to read back, and things are generally more by-the-book than the US. In practice, very little difference, though.
Outside controlled airspace, it's completely different. At airfields, in America you'll use Unicom, where you self-announce, talk to other pilots, and have to be aware that you may be sharing the frequency with other airfields. In the UK, you'll have an Air-Ground service, with a dedicated frequency, and an operator on the ground who can provide you with information (but not instructions) to help you use the airfield safely. The UK also has the concept of AFISOs, there's no equivalent in the US.
En-route outside of controlled airspace, the US has flight following. In the UK, you can use either FIS or RIS for similar (but not identical) services. The US has no equivalent of RAS, since there is very little IFR flight outside of controlled airspace.
There - that's a start. I'll let someone else carry on!
FFF
------------