Yes, the power from AC cord or generator should be the same. The transfer switch chooses which you get but it is the same otherwise!
They call them red and black as I assume that is the wire color but one will be feeding the front air and the other will feed the rear!
Click this snip to see better or go direct to this drawing for a whole 110AC layout:
https://www.winnebago.com/Files/File.../000218585.pdf
If the breakers on both are good, the next most likely place I would look would be the transfer switch.
But the connections at any point along the line including at the Generator should be checked. Are there two breakers at the generator or one combined to operate both feeds?
But there are often better ways to start looking for the problem!
If we find the one Air unit is not working, it may not be a problem with the input power as it takes lots of other parts as well. Perhaps something as minor as a bad thermostat?
But we can save trouble of digging into the transfer switch, etc. if we do some easier looking first before deciding it has to be a major power problem.
You have what looks like loss of one feed? But have you checked that idea?
If you have two feeds for the whole RV and lose one, that means about half the RV 110AC will not work! So is half the RV dead?
I would guess that would be noticed but not if we get focused on the first item we find dead!
If about half the RV is dead when running on Generator but live when plugged, then look to big feed problems. But if you find it is only one Air unit that won't work, it is not likely to be the main feed!
Maybe only a 12Volt fuse as that runs the controls?
It's always good to first define the problem and let that lead to where to look.
In the case of the air, there are so many small points that it is much less likely to be in the big parts if we have not noticed any big disruption of things!