It's a tough question.
From the MS support, "corporate push" perspective, C# is definitely newer, and more likely to be in vogue. For a while MS thought they could kill C++ for Windows development (which would have made your choice very easy), but recently they have been coming back to the idea that "real" apps will continue to be written in C++ for various reasons. So, I see it as 50/50 in terms of future Windows development support (slightly favoring C# though).
As a few people said, C++ certainly opens more potential job avenues, with multiple platform support and variety of applications. You probably also want to consider the type of apps you're going to be employed to write: C++ will be more hardcore, run everywhere, or legacy; whereas C# will be more internal tools, web services, or client UI. It's a toss up for number of opportunities, but personal preference could push the decision to one side.
If I were you, I'd look for a job which allowed (or preferably paid you more) for your ability to do both, but admittedly that's kinda a cop out. I see C#/C++ as 50/50 for future Windows development at this point, more or less.
Addendum: I write both in my job (although I focus on C++), and my company would pay more for candidates which had knowledge of both. However, we would be more likely to hire a C++ programmer with C# knowledge rather than visa-versa, because there seem to be far fewer bad C++ programmers these days than bad .NET developers. Just an observation which might be relevant.