"Both were tripping one of the two 30A breakers on the gensets."
Are these contractor style generators, with open metal frames? If so, you're typically limited to half the total generator power on each leg of a 240V split-phase circuit. Depending on how you're plugged into the generator, you may be only using one leg for everything. Depending on how your RV is wired, you may have most loads connected to one leg.
The breaker on the generator is popping simply because you're trying to use too much power from that leg of its output. The shore power breaker doesn't pop under similar usage because it has a higher capacity and can support the load. There is nothing suggesting any fault in your transfer switch or other part of the RV in this case--simply that you're trying to use too much electricity from the more limited source.