I have a homebuilt desktop (core components were upgraded 14 months ago on a <$800 budget) and a 2011 13" MBP. In addition to gaming, my uses include programming/software development and image manipulation (Photoshop), and I'm very satisfied with this combination.
My brother has a top of the line 2011 15" MBP. While it can run most newer games, it's still significantly slower than my desktop where gaming is concerned, despite the fact that said desktop is now over a year old and has a mid-range GPU (Radeon 5770). Towards the end of this year I will likely replace the 5770 with a next generation high end card (for all of ~$250 at that), and the aforementioned comparison will then border on absurdity. Because powerful GPUs will eat up a lot of wattage in short order and put out a lot of heat to match, they don't pair well with mobile platforms and thus there's really no alternative to a proper desktop if you have any serious interest in gaming.
Besides, it's nice to have some level of redundancy in a worst case scenario. Laptops are relatively prone to theft and hardware failure (though you can certainly mitigate the risk of the former to a very low level). Oh, and definitely build the desktop yourself. It's really pretty easy these days (what with the vendors themselves matching parts for you, and every major hardware site out there offering build guides) and you'll get better parts for the money. Putting it together can be fun in its own right, if you enjoy tinkering.