Las Vegas

It really depends on what you like to do. You'll get VERY HOT weather and COLD A/C in Vegas. You will also probably lose money if you gamble but can make up for it with the free drinks (which can also be a problem). There is never a shortage of things to do as the nightclub scene has never been hotter. Try the Rio hotel or Caesar's Palace if you go. All of the Cirque du Soleil shows around town are great - I like the one at Wynn for the small theatre and the more adult one at New York, New York. Rita Rudner is really funny at Harrah's. Over all not an inexpensive place to visit but the strip is only 10 minutes from the airport and it's easy to get around by walking or taking the new monorail.
The real New York (Manhattan) could have uncomfortable weather as well if the humidity is up. There are GREAT shows and museums - again somewhat pricey. Can't speak much about the nightclubs but I'm sure there is no shortage. Like Vegas, you'll just want to walk and look at the buildings and the people.
I might choose Vegas over Manhattan just because, once you're on the strip, everyone is there to have fun - you don't see much of the real world while you're there. NY is, on the other hand, a regular busy, busy, busy city where people have their own lives and customer service is not a high-priority unless you are in a really nice hotel or theatre or restaurant, etc. Otherwise, you're just another tourist. That being said, you really do have to visit NY at least once - it is an experience.
Probably hasn't helped you decide but it was nice for me to remember my trips. Good luck deciding. Look around the Internet for specials on shows, museum passes, etc. before you go once you know where you are going. It can save you some $.

My impression of Vegas was its like an adult Disney World. Gambleing, nightclubs, shows, shows, more shows, glitzy shopping, a variety of restaurants. Like an adult playland and sort of unreal. New York in contrast is very real, very big, and the energy is just as high. The shows, shopping, ect have mmore substance to them if that makes any sense. Personally I like them both. If you are lookining for culture and big city my advice is to go to New York. Even spending 6 days there will be a great experience.