Being a bit special needs, I actually have both and they’re both good – I’ve yet to find a frame that doesn’t fit the 591 from my Son’s 20″ wheeled bike to my Cove, my Wife’s HT and my mates road bike, obviously not having to stow the front wheel helps, although I’ve got a wheel bag to keep the boot clean(ish), the only downside is that a friend used one and the frame managed to fall out of the clamp, we had 3 bikes on the roof at the time and we were all working together loading up and I suspect it wasn’t put in properly – anyway the bike fell, made a dent in the roof and scared the crap out of us – but the wheel straps are good enough that it won’t fall off completely.
The 561 is almost totally secure, especially with a 20mm / 15mm fork (bear in mind that they come suitable for 20mm or QR, if you’ve got 15mm you’ll need an over-priced adapter) but of course you’ve got to stow the front wheel – it’s not usually a problem, but if you’ve got 3 in a car and say driving to the Alps, 3 wheels take a lot of room – also the 20mm doesn’t fit Rockshox 20mm forks with maxles they’re a couple of mm too wide (they fit Fox and Marz 20mm forks perfectly) so you’ll need to get the metal file / Dremel out to trip them a tiny bit – doing so doesn’t effect the way they fit other forks.
Typically if we’re going on a long journey with 2 bikes I fit my wife’s HT onto the 591 but in such a way that the open side is facing into the car and not out, then fit my bike on the other side with the 561 – so if my wife bike does fall out, it just falls onto my bike – it’s never, ever happened, but that one time on my cars car 5 years ago put me off. As for carbon frames, there’s quite a bit of clamping force with the 591, I perhaps wouldn’t fit a light road bike into one, but I suspect a mtb would be okay – bit of a risk though.