Alienware is very powerfull. But only for what is it, half an hour on battery?
And I believe they are generally more expensive. (correct me if I'm wrong)
For $1200,- you can get a beast of a laptop, but more of a beast of a computer.
Perhaps what you could do, is spend around 800 on the laptop (you can get very nice laptops for that money) and the other 400 on upgrading your desktop hardware if necessary. 8GB of (extra)RAM costs about $50 currently? and a very good GPU card can be found for around $300,-