We have just bought a motor home having been caravanners for 25 years. We have towed caravans to Europe and been as far as Austria when the kids were young. With a caravan, the van size and weight determines the size and weight of the tow vehicle. Basically the car needs to weight 100% and the loaded van should not exceed 85% of the weight of the car. When we bought our first van we immediately had to get a bigger, heavier more powerful car. The combination of decent car and caravan, even secondhand will approximate to the cost of a decent motorhome secondhand so you pays your money and takes your choice.
The caravan is good for parking up for a reasonable stay, putting up an awning etc and leaving on site whilst you retain a car to drive around in locally when you get to your destination.
The motorhome is an all in one accommodation/vehicle combination. When you get there you have to still drive around in it unless you decide to tow a little car like a Smart or something similar. Europe is geared up for motorhomes and is more motorhome friendly than the UK.
You will get a higher load allowance on a motorhome than on a caravan. A caravan requires careful loading to get the balance right to avoid snaking issues. There are lots of issues with UK caravans and leaks/damp so choose carefully but some are OK. I like the look of Buccaneers as a quality product. You will pay through the nose for an Airstream.
I have an 2010 Autotrail Frontier Savannah bought recently with less than 10k mileage, a 3 litre diesel Fiat cab and good quality fixtures and fittings. It is dead easy to drive and very much like a car in terms of steering, clutch, gearbox etc. Think 3.5 ton white van. It creaks and rattles a bit but you learn to pad out the crockery with foam etc. Fuel consumption laden is affordable compared to American gas guzzlers which will cost a fortune to run in Europe unless you can always bank on filling up in Luxembourg.
Height is also a factor and 3m is an important limit not to exceed. I have not been abroad in it yet so have not looked into the ferry pricing. Having run the biggest Volvo estate and a Bessacarr twin axle large caravan on cross channel ferries I can't imagine a motorhome can be more than that.
European motorhome cab based coachbuilts have the habitation door on the wrong side for driving in the UK but obviously on the right side for the continent. Ovens tend to be small and very high up which is not safe for shorter wives. I don't think Europeans use their ovens very much!
There are some very impressive large A class motorhomes like the Carthago, Hymer, Niesmann & Bischoff etc but they are very big and very expensive and no doubt suffer from depreciation.
Be very careful to get the layout that you want - don't buy other than for yourselves i.e. don't assume that friends, children/grandchildren will come with you. An awning can cater for them. With a motorhome make sure you get one with the right number of belted seats for the beds & passengers as they tend to have less belted seats than bed spaces!
Come back with any questions
