Assuming that the HBO HD broadcast was 1080i HiDef, then the video quality should be much better than a DVD (only 480p). Audio should be about the same since both are Dolby Digital 5.1. But, as Steve points out, there can be lots of other variables. Why do you ask?
Sony SAT-T60 120GB (v3.5b)
HR20-700, HR20-100, HR21-200 HD DVR
HR10-250 HD DVR 400GB (v6.4a)
H21-200 HD Receiver
R10 DVR 160GB (v6.4a)