Okay, here's what I have to say about your question:
1.) Stay the FUCK away from ANYTHING that even looks like Alienware. They are terrible computers, and, aside from one, every person I know that has bought an Alienware computer (laptop or desktop) has regretted it, because it's vastly underpowered for more money than competitors. Seriously. ASUS makes decent gaming laptops though.
2.) Your question can really be answered by answering this question of mine: Do you move around a lot? Like, travelling? Or LAN parties? Then you should spend more money and get a gaming laptop. They're heavy, get very hot, and, while they can usually be upgraded (Look up MXM video cards...), you usually won't want to, because parts for gaming laptops are often the price of a regular laptop themselves. However, if you're going to be in one spot for a long period of time, like at home, or if you're staying in a dorm room at school, a desktop is the better way to go. They're MUCH cheaper, can be easily upgraded, and don't fall behind the tech curve as fast as laptops can.
3.) Gaming laptops are not underpowered, provided you're willing to spend the money to get an up to date one. They cost several thousand dollars, have TERRIBLE battery life (Like, less than an hour.) and they will fall behind in performance as time goes on.
4.) If all you care about is gaming on the go, you can get laptops for cheap that aren't meant for gaming, but still are capable little machines. A friend of mine has a 15" HP dv5, quad core Phenom II, Radeon HD 5650 graphics, 6GB RAM, and while games aren't played at the highest settings, it can hold its own.