We have a twin axle Abbey which we bought from new two and a half years ago. It's heavier than a caravan with a single axle so the towcar uses more fuel and in terms of stability it's no more and no less stable than a properly loaded caravan on a single axle.
After a few tows you don't really notice much difference, reversing is easy enough although it helps to have the o/h keeping a look out behind when reversing just to be on the safe side. You have to bear in mind that the back of the caravan can swing wide when turning, care needs to be taken in traffic where there is more than one lane such as at busy traffic islands.
Servicing is more expensive on a t/a caravan.
I wouldn't fancy trying to manoeuvre our t/a by hand, its possible to move the hitch across a couple of inches by hand to get it to line up and I always reverse our caravan using the towcar so I save on the added weight of a motor mover.
Some continental t/a caravans are excluded from some sites but as far as I know most sites are happy to accommodate t/a caravans.I use a lot of certified sites so I always mention that the caravan is a t/a when I contact the site mainly to make sure that there are no really tight entrances. I think that Haven holiday parks might levy an extra charge for longer caravans but I don't use Haven sites anyway.
The advantages of having a t/a caravan outweigh any disadvantages as far as we are concerned, we like plenty of room to stretch out and move around. We once owned a Lunar Meteorite which we loved and we had many happy times in it but the after the sheer luxury of a fixed bed and roomy end washroom with a large separate shower I'd never revert back.