If you want a modern caravan whether its twin or single axle is dictated by size of caravan. If you want largest possible 'van you can legally tow with a car then you have to go for twin axle. Smaller than that but still quite large then they are single axle.
Twin axle is a factor to consider if you intend going to France. I saw several sites this yr that have added large extra charges for twin axle 'vans. 'Gens', ie travellers are a big issue in France at the moment & high extra charges for twin axles are being imposed for same reason as some UK sites have signs 'No Hobbys or LMC caravans'. Having said that, plenty of Brits do tour in France with twin axles & are ok on most campsites, so shouldn't be a problem.
We went to the Essex Country Show at Barleylands over the weekend, we were exhibiting there with two of our engines:
We used a 4-wheel trailer for the smaller engine.
Despite very wet conditions we had no traction problems on the grass at the show, and everything went well over the two days. We packed up Sunday evening and came back Monday morning.
Next show is at Little Casterton near Stamford, a nice little show if you're interested in seeing old working machinery on the land.