As bwarbiany explained, the over that air broadcast is not compressed like the satellite feed is. It made a huge difference.
FYI, the OTA is usually not compressed AS BADLY as the satellite feed is. All signals are compressed using industry-standard algorithms, but not all compression is equal in the way it's implemented.
If you've ever ripped DVDs to video files (or even just CD to MP3), you'll know that every compression program will have settings that is always a balance of video/audio quality vs file size.
Satellite and cable are trying to fit as many channels as possible into a single limited-bandwidth cord, so the tighter they squeeze the quality settings, the more content they can provide. IPTV and streaming providers are only giving you one "channel" at a time, but they also know that internet bandwidth isn't free or unlimited, so they have incentive to squeeze it as much as possible as well.
OTA broadcast has a band of spectrum allocated. If they use 100% of their allocation, it doesn't hurt them or cost them extra. So they have more incentive to optimize for picture quality in their compression.
For most things I'm watching, I just let Hulu stream it to me even if it's on a channel I can pick up OTA, because honestly it's just easier. But for sports, if it's OTA I default to the antenna. The picture quality difference is immediately noticeable.