I prefer American drama mostly because of the way it's written and filmed, it's usually very stylish. At the moment I'm loving Bones and Cold Case. Yes, they are a bit dumb in a lot of ways - they fit a lot into an hour that would really be spread over about six months of detailed investigation, but they have such a cracking pace and suspense about them. British cop dramas tend to lumber along, very sweet and quaint but without any pace.
American dramas are team efforts when it comes to writing - although it usually has a 'written by...' on each programme he/she is the head of the team - they have more people working on dialogue so each character has a very different voice, whereas in British drama there are stereotypes written in because there's usually one writer trying to write in different voices.
Also American dramas are filmed week by week so are only about three weeks ahead of when they're shown, even for a 26 part series. So they reflect the seasons so much better and seem relevant, they can react to politics quickly. British ones are written and filmed in series then shown after filming has ended.
Another thing - and by this point I bet you're thinking 'she's studied this far too much'
- they are filmed very stylishly, they use fast camera techniques and more hand held cameras so that there is again that sense of pace.
Sorry, bit of an anorak I know but what the heck, you asked!