I've done both degrees so i'll let you know my experiences of both :
Games development : you'll get a broader view of games development and what really goes into making games, you could also be involved with all aspects of the game - art, code, design, QA, management, music etc. you'll probably do lots of different modules, learn how to design a game, write design documentation and then make a game in a team.
Computer science : you'll most likely be doing core programming and making a game using a given language, or developing a software solution for a business but either way it's pure maths and code.
The career path and opportunities will be slightly different. Computer science opens up programming jobs pretty much everywhere. Games development is good for artists and designers, for people that know they want to specialise in 3D character modelling, become a games designer or for people who haven't quite decided and want to taste all aspects of game dev and see what it's all about. Games development could also get you hungry for indie gaming, you might want to make a game on your own.
I don't regret doing either one, they taught me specific skills that have helped me in the industry. When games jobs said they required a computing or engineering degree, the games development one was enough for this. I would say pick computer science if you know for certain you ONLY want to be a programmer (my guess is if you do, then you already know this). If you don't know yet but like the idea of games design and development then do the all round game dev course.