I use an old school, loud, stinky and annoying generator from time to time only on my own land, far from neighbors, of if I need an excuse to run it at home and my camper happens to be here, I'll plug it in and run it for a bit just so my old generator doesn't feel too neglected from lack of use.
An inverter generator produces cleaner power, and they are almost always quieter. For camping use, you can get models that supply all the power you ever would need. If you needed a LOT of power from your generator, well you pretty much are stuck with the old school variety. I've seen some in the 50,000 watt range.
More info from Yamaha on the subject -
Conventional Generator vs Inverter Generator
Edit - Sorry I just threw that link out there without giving you my own personal opinion on the matter... which is. If I were to buy a new generator now... it would be an inverter generator. Typically less noise, you can plug sensitive stuff into it if you need to (sine wave is better(i.e. pure)) and I believe most, if not all of them - also provide DC power plugs in case you just want DC power directly off your generator. And just to add, that link above isn't from Yamaha afterall, I was fooled by the URL, good information there none the less.
The inverter in your camper is COMPLETELY different than the one in the generators we're talking about. It converts DC from the battery to AC in your outlets, that's all it does.
Your generator already puts out AC.. the inverter in the generator is just used to clean up the power and it actually converts AC to DC and then back to AC again. I know it gets confusing.. but 2 completely different inverter types are in play here.