Very little difference. With a rear wheel drive you increase traction on the drive wheels with the load on the towball but it reduces the traction on the front wheel. Whilst thsi is unlikely to be noticed on the road except on a steep hill start, it can be most noticeable on wet grass.
Overall I have noticed very little difference when I changed from rear to front wheel drive.
On a wet or muddy field is where the difference would be noticed.
My own experience with FWD is that when the car loses grip it is more likely that the front end will slide around "polishing" the grass, the wetter it is the more likely it will dig in.
From watching RWDs in similar situations, they will have more grip but are more likely to dig in.
Whichever I had in those circumstances I would probably seek help from a 4WD and that has happened once in 3 years and c.50 rallies and CLs in all weathers and with more than half of them green field.
We had a Shogun for a while but the extra running costs were not really justified for the amount of times we needed 4WD - and the Alhambra we have now is a far better and more comfortable tow car on the road.
Once again, there is little difference, both will slip without due care. However, ask yourself, muddy field, car parked alongside the caravan or attached to it, waiting to move off, which wheels are close to the tarmac road and hence safety?