Thinking about how it works, a signal is a signal. You have the frequency, power, and its spread. The difference could be that there is much more bandwidth with an HD signal, which might make it more susceptible to disruption given distance, not due to the distance itself, but potential obstructions within the distance travelled.
So on a flat plain, the signal would be about the same for a given distance, but in the real world with obstructions, the digital signal is taking more losses.
Oddly enough, after I put in a newer Smart Card, my OTA signal appears to have improved, but that might also be fall. I went from scattered signals on some channels, to near perfect on a few and very reliable on others. Also, with the latest rescan, saw there are even more sub channels. No idea what is on any of them with no guide, but it is nice to have the illusion of more programming.