The main thing is the white patches on the ends of the wings, which are visible on both birds. Black vultures have entirely black wings except for the white patches. Turkey vultures have black on the front parts of their wings, but the back parts are lighter. Note that the patches on black vultures are actually white, and on turkey vultures they are just lighter if that makes sense. Black vultures also have a different shape with different wing beats, as well as a shorter tail. I don't have a ton of experience with them but I've always found their shape and wing beats to be slightly bat-like.
As for the birds at hand, it's difficult to make an ID based on the information you have of their flight. I might say waxwings have a slightly more erratic flight on average than cowbirds, but I don't feel confident putting that out there as strong evidence.