Gaming notebooks have their place in the market, and I would recommend the Alienware option if you were a gamer who moved around. If you were going to LAN parties, or friends' houses to LAN, then the Alienware notebook would be the way to go, but for you, I would recommend the desktop.
Power-wise, it will use a little bit more, but if you purchased power-efficient hardware, it shouldn't be too bad. You could get yourself a great Core i7 system, with a GEFORCE GTX 680, and have a much, much faster system, all while costing less!
Considering the system you're using is being used as a standalone box, with projectors and audio systems plugged into it, a notebook seems really out of place. A desktop on the other hand, would feel perfect, drop it down somewhere, plug it in and go!