I'm currently a major in game programming at my college and it's been going pretty well. I have an internship for a mobile development company and I have an IDGA (international game developers association) membership. However, I have friends who major in other degrees (such as Computer Engineering) and currently are out in the indie world doing great! It all depends on where you go and who you know. Gaming schools are better to network with other people in the industry, thus opening a LOT more doors. Although you could probably get very detailed knowledge with other degrees such as Computer Engineering. So honestly it can also depend on if you just flat out want to be in the gaming industry and nothing else, or if you want to be an ENGINEER, and the gaming industry is something you want to do for a bit in your life, but not for the rest of your life.
So in MY opinion:
Gaming related degree - more networking opportunities, more open doors to get in the industry
Programming related degree - more in-depth knowledge of computer science/engineering, more opportunities other than this industry
Hope it helps