If you're trying to get a computer for gaming, go with PC and go with a desktop. You should also forget all about Alienware and just build your own or if you don't want to learn how/take the time find someone locally that will build it for you. Failing THAT, check out websites like ibuypower or cyberpowerpc (not sure if those are reputable now, but my old roommate had a kickass PC from cyberpowerpc for at least two years that was almost as cheap as DIY).
I say this because I had a laptop about five years ago that was designed for gaming and I always, always, always had heat and battery issues. The power you're gonna have to put out to play modern games at high settings is just too much for laptops. If you're going to plug it in anyway and have a place where you can mount an extra fan or something...then buy a desktop and a cheap laptop for travel/school/whatever.
Whatever you do, don't blow tons of money on Alienware. They are way overpriced and you're just paying for the name.
Edit: Oh, and I feel the same way about Mac. Paying for the name, basically. Well, unless you're doing graphic design and such like the above poster said. Then you'll probably come out cheaper in the long run.