Hmm well, you didn't tell us what you want to do with it, and that makes a difference.
As mentioned previously, the Alienware has a couple of hardware advantages that relate to gaming, such as the HDMI port and the option to get a better video chip. The Mac video chip isn't bad either, but honestly as a non-gamer, I would never be able to tell you whether that is good or bad. I can tell you that I've owned a number of Macs and PCs and consistently, the Macs are more stable and smooth on graphics of all kinds, especially everyday kinds, like browsing web pages, documents, and massive libraries of photos and videos.
Don't listen to anyone who says that there is a huge difference in hardware. Actually there may be- the Alienware hardware is huge! More than twice as thick as the Macbook Pro, as well as twice the weight. The AW doesn't advertise a battery life figure, but Apple credibly alleges 8 hours. Users say expect an hour max from the Alienware, aka the battery is just in case you can't tear yourself away from it for a bathroom or food break.
On the other hand, both use the same Core 2 Duo processors, although the AW is available at substantial extra cost with a Core 2 Quad. The AW uses higher end chips from the same manufacturer, Nvidia. You can jam them both up with huge hard drives and ram, although the AW actually leaves room for a second hard drive so you can literally fit twice the space in it. I don't see how a MBP with a USB hard drive is any less portable than a 12 pound, 1 hour battery behemoth, so I wouldn't call this a real advantage.
So what it comes down to is compromise. If you aren't a die-hard Windows enthusiast, you'd be a fool to plunk down all that money and not end up with a quality, user-friendly, reliable machine running Mac OS X. If Windows and Windows games are the be all and end all of your existence, then the AW may be a good choice, although you might at some point get laughed at by a peer who bought a Macbook Pro for the same price and can play the same games without having to root around constantly for an outlet and a table. Since you can use Boot Camp (for high performance games) and VMWare Fusion (for office and routine applications) to run Windows 7 just fine on the Mac, you can't say that there is some kind of application advantage to the PC, because the Mac can run 100% of all Windows applications, plus run 100% of all Mac applications and most Linux programs as well.
Another difference to consider is the ergonomics. Which is of course important on a machine you will spend a lot of time with. Both have backlit keyboards, one is red and the other is blue-white; you have to decide which you prefer. There is a difference in trackpads; the Macbook trackpad is huge and centered, but the AW trackpad is tiny and off to the left. If you ever intend to work or game without an external mouse, that may be an issue. However, the AW has a numeric keypad, which the AW does not. I like how my Mac's keyboard is centered relatively to the screen, but this is a personal preference.
So in conclusion, if gaming while staying in one place is the absolute priority, then the Alienware has some advantage from its somewhat improved video card specs, and somewhat improved processor if you go to the maximum of all specifications. This will result in a net price over $1200 more than the Macbook Pro, that is, enough to also build a formidable desktop computer to compliment your laptop.
So actually, I would have a very, very hard time recommending the Alienware to anyone. I recommend the Macbook Pro.