In general, DirecTV takes the OTA signal and then converts it from MPEG-2 to MPEG-4 encoding. This conversion is a "lossy" process and so the DirecTV picture can't be better than the OTA picture. If the encoders are set up correctly, you can't really see much difference. Generally though, the DirecTV picture quality will be slightly worse.
There's one exception. In a city where DirecTv gets the signal via fiber, instead of off-air, and where the station has subchannels, which steal bandwidth from the HD channel when it is transmitted OTA, the DirecTV picture quality can be better.