The last time I watched OTA/Cable was over a decade ago. I remember paying $120/month for cable, and getting low quality highly recompressed HD shows, which looked terrible on the 1080p TV I had at the time. Digital artifacts made the stream not very pleasant to watch at all.
Technically it was "1080p HD", but in reality it was more like 720x480 upscaled and smoothed.
Digital cable is generally more heavily compressed than HD OTA primary channels (usually x.1 subchannel). OTA only gets bad when they pack in too many subchannels.
Technically it was "1080p HD", but in reality it was more like 720x480 upscaled and smoothed.