OpenGL's primary positive points (to me at least) are it's easier to learn, and more portable, it's available for Win32, Linux, Mac, etc.
Direct3D tends to have far better driver support. The API progresses at a much faster rate than OpenGL. As new hardware features becomes available, Direct3D will more than likely support them before OpenGL. The D3D API in 7 is a lot cleaner than earlier versions, and there is a utility library, D3DX, which can handle most tedious chores for you, so the ease-of-use factor is greatly diminishing. I picked up D3D in about a day.
There are a few performance factors, such as Direct3D allows greater control over texture management, however these should not be a big factor on a beginning D3D programmer.
You're best bet is to probably try both API's, and then pick which one you like best.