I personally don't like the 'hang on' type - I used a Saris Bones once and it was a faff to set up and didn't feel that secure, albeit it took the two bikes it was designed for and didn't fall off. However, the straps loosened on the relatively short trip (40 miles) I wouldn't want to go a long way with one. It also covered the rear numberplate, so although the (hired) car had no socket for it, it needed a lighting board really. I winged it without one, planning to play the naive card if I was pulled, but I wouldn't want to do it often.
Roof ones are much more secure, but worse for fuel economy and you have to lift the bike higher to get it on.
The 'ideal' solution is a tow ball mounted rack - they're stable, easy to fit, keep the bikes in a relatively good place in terms of aerodynamics - you do need a tow bar, but you need the electrics for many of the strap on racks anyway, and depending on your car you can probably get a secondhand tow bar from a breaker and get an arches mechanic to fit it quite cheaply - I paid a mobile guy £60 to fit mine.