cable/sat and antenna all get the same feed from the same source. (Not necessarilly true, I beleive for instance TVO sends a different feed to the rest of the province transmitters and they use shaw direct for that)So technicaly they can be exactly the same (and even in theory anyone can be higher) (Not OTA , it is limited by the bandwitdh of an ATSC channel , that is 6 Mhz, sat/cable could change those internally).
But to understand the topic the best way to start is from the beginning. Let's say someone is watching Hockey Night in Canada (since we are Sat and in Canada). CBC sends a "high quality" feed to all the stations from the arena (from the arena it goes to CBC master control , I would assume, and then it gets "produced" and distributed), the station gets it and adds local advertisement and stuff and you get your CBC station (for example in Toronto I think it is ch.5 for OTA) now technically it could be possible to get a direct signal to the cable/sat companies and not be limited by the OTA BW/specs, but what really happens is that the Cab and sat companies get that same OTA signal. Since they work off that channel they are limited by that channel. Now they get CBC Toronto as well as many other channels and they need to send them down the pipe to you and everyone else. So what happens is the cable /sat companies take that signal and re-compress it and that is done unevenly, some show/channels are compressed more than others depending on several factors. (exactly butthey do not say that on their ads ,or do they?, sorry but english is not my native language, lol)
That is why people talk about OTA being higher quality (because it acctually is, period). Is it necessarily always there? no, is it a lot or a bit when it is there? that depends on the difference and how much you care. (it depends on so many factors acctually, and yes everyone should care)
I think the biggest reason people talk about it is that in the old analogue days the cable & sat companies had fine tuned directional antennas to get the signal and so Joe with his rabbit ears was getting snow, ghosting ... while the guy receiving cable/sat had a clear image. This has engrained the notion in many that cable and sat must look better. So people feel the need to point out that not only is it not true but that the opposite is true. (and now that you mention analog , hold your horses, because a good analog signal could blow out of the water almost any digital version you see out there, ask the japanees @ NHK about their Analog HD trials)
As I have said before it is all about how the technology is implemented. Unfortunaelly it is all about maximizing their profits at the cost of quality for the end user, but heck we already knew I was so naive even to expect otherwise, lol.