You really won't be disappointed by either!
Cost: While Amsterdam is among the more expensive cities in Europe, London takes the cake for us North Americans and our lousy exhcange rates on the pound.
Stuff to see: London's HUGE and you couldn't see everything there in a week if you tried, because there is a fuckload of cool stuff to see. Amsterdam's relatively small, but it has unique features like canals, narrow gabled houses, and cute girls on bicycles that give it a distinct charm.
Partying: London's got a world-famous club scene, where there's some party crackin' any night of the week. Just remember to bring your £s! The bars/pubs are great, as well, whether you want a rowdy student scene or hanging out with the oldies and playing darts. Amsterdam, while it has some great clubs, is more subdued, and it's more of a weekend-only affair. However, the bruin cafes
are a great way to kill hours drinking little beers and chatting with the super-friendly locals.
People: A lot of people in the UK will rail on London (as will anyone about their largest cities) because the people can be more rushed, brusque, and not as friendly. While I've found that to be largely untrue, at least, no less than any large city, I'd say people in other cities have been more
friendly. Like MeTurk said, Amsterdam's not your typical capital city - it's smaller, the pace is more laid back, and the Dutch are so damn nice. The only people I didn't like in Amsterdam were all the drug tourists, mostly yanks
The verdict: Do both! Because of the airlines I prefer, I typically fly into London and use it as a jumping-off point for the rest of Europe. I'll fly into Heathrow, typically hang out in London for a few days, then jump on a flight elsewhere. If you want to put London at the end, you can fly to AMS cheap on BMI, hit up the continent, then come back to do London before going home. If you want to start out with London, hang out in the city, then get to whatever airport is offering the cheap flights to wherever. In my opinion, doing the Heathrow-bus-Stanstead/Luton transfer in one day isn't worthwhile...