When bagging the bag weight causes a weight shift to the rear thus loss of traction on the front wheels.
Rear drives have smaller discharge chutes which clog easier.
With walk behinds deck size makes a big difference so go with the biggest deck that will fit between your smallest space.
One extra pass on a ride on is nothing.
One extra pass with a push mower is a lot of walking & even more time.
If it were me I would be looking at 2 mowers.
dedicated mulchers do their job really well.
Universal decks universally do neither job particularly well.