I am 30 years old and am returning to school after receiving an incredibly useless degree in liberal arts. I have been very interested in 3D animation (games, movies, advertisements etc.) since I was a teenager but had previously been too hesitant to enter the field or even the classes at school due to personal doubts about my potential ability.

I have realized I am no longer a youngster but also suddenly have the opportunity to either enter a degree program that focuses on the art and animation side of game design or one that focuses more on the technical side to game design, mainly programming. I have some experience with the art portion and practically no experience with programming outside of a little HTML and VRML which no one uses anymore.

I guess my question is, assuming I am able to show promise in either, at my age which of the two would have better potential to lead to a career after I am finished with the education?

If you had no experience with programming then I rather propose animation. I've started to interest with 3D stuff late too. Just few years earlier than you
I've been meeting people older than you startig with this stuff too. Usually old graphics who wants to start with something new, to extend their capabilities of their creation process