Hello Andy,
Without any doubt, the inverter type generators are better and safer than the undetribalised types. The none inverter types can over speed when a heavy load disconnects and that can cause a voltage spike that may damage sensitive electronics.
which ever type of generator you go for, they do produce noise, and they are hopelessly inefficient at converting expensive fuel to useful electric power. The best a small generator can achieve is about 8%, and more typically only 4 to 6%!
By comparison your gas appliance have to be at least 70% efficient. So you can run your fridge, heat water and of course heat your caravan using gas.
If you are frugal with your electrical power the battery will last more than 4 days. If you are concerned buy a 60 solar panel and that will usually replenish a major proportion if not all of your you daily power usage.
I am not dead set against generators, they have their place and uses, but there may be realistic alternatives for most caravan users.
If you add up the cost of buying a generator and the fuel you need to run it, (Not to mention servicing costs etc, you can actually buy quite a lot of gas.