Generator vs Battery/Inverter/Solar

Higher voltage will not harm flooded lead acids, though they will go through water a little quicker. But it will eventually harm AGM batteries, and pretty quickly ruin gel batteries. For longest life you want a proper 3 stage charge, with set points for the battery chemistry being charged. Another peculiarity of AGM batteries is their life will be shortened by chronic undercharging - which is actually more likely in a camper. They need to be fully charged periodically to maintain capacity. There is a new type, carbon foam AGM, which does not suffer this effect, but they are expensive.