I would love to visit either city! I think you need to consider 3 things:
- the length of your trip
- the amount of money you can/are willing to spend on it
- what you want to do while you'r traveling
Rome:
I think that if you are looking for a more "eurpoean" experience, you should definately go to Rome. You will also be closer to other cities/regions you might want to visit. Loads of historical stuff if your're into that. Shopping will be less expensive over-all. Great food, as everyone's said.
You will exposed to a very different culture.
London:
If you're just looking to go out and have a great time, you might consider London, because you won't struggle as much with language barriers. The city is very hip and urban (according to a friend who currently lives there), has a lot of public transportation to get you around, etc. If you're into the theatre and things, that's a plus. Shopping will be more expensive and probably more trendy. You will probably feel more comfortable in regards to the culture. (But that depends on how you adapt to that sort of thing, also)
Let us know what you decide! You'll have fun in either city, I'm sure!!!