Update:
Based on a couple of the answers I have received, I just want to make clear that I am well aware how to go about mocking HttpContext using a moc
I'm leaning towards HttpContextBase. Mainly because I think it was invented for just this reason: testability. And why reinvent the wheel when there's an acceptable solution already out there.
If you put a lot of effort into your wrapper classes around HttpContext, you'd end up with something very similar to HttpContextBase...