DVD is 480i or 480p (720x480) and depending on the source the Direct TV channel was using it could be UP to 1080i (1920x1080).
So without getting into a long post about the diffrent compression standards and such it is fair to say that the HD TV version should be much better then the DVD.
It depends on how you recorded it. If you used a VCR or a standard definition DVR or TiVo, it won't be any better than a DVD, and probably worse. If you recorded on an HD DVR, then it may be better.