Well - mens restrooms are cleaner when it comes to the toilet seats usually, as long as there are urinals there - those are smelly then, but if they would be in a separate room or something, I would not care

- as long as men do not try to aim into a regular toilet bowl... But yes - since most women seem to hover as squat over public toilet seats, those can be a bit messy, too, however its harder for women to really mess up the floor all round the toilet.
I think anyways, the best wouold be to use the asian or southern european variant for public toilets

I know this looks uncomfortable and I would not want to have this in my home, but honestly, it is a lot easier to squat and hover over those compared to trying this on regular seat toilets which are dirts anyways in public toilets.
They should provide toilet paper though, unlike in some asian countries

Oh and of course, if i use a mens room because the womens room has a long waiting line, we usually stand guard

- so we do not really like to use it while men are actually in there as well, unless it is really an emergency pee situation

. Usually men just laugh at it, knowing about the problem of the waiting lines - I never had a man complain about a woman being in the mens room, but depending on the situation (and alcohol levels) they can sometimes make sexual remarks, which is annoying...