I definitely have an overall higher cadence when "road riding" (this would include paved/unpaved roads, rails-to-trails, city bike paths...) vs "mountain biking" (i.e., single-track dirt). But it has nothing to do with the bikes themselves (fit or size of the wheel/tires). I am pretty sure on the road I have similar cadence whether riding my road bike or my 6" All Mountain MTB.

The difference has to do with two things, both related to the terrain:

First, it is a lot more practical and possible for me to maintain an "optimum" pedal cadence on the road. My speed is not constantly and dramatically changing like it often is riding single track. What I find when mountain biking is that unless I want to be shifting nearly constantly, I am going to have a widely varying cadence (as it is, I already shift more when mountain biking than road biking). And what I also find is that being below the optimum pedaling cadence is better than being above it. I can always stand and hammer through a short low-cadence section (which may only be a few seconds). Not much I can do if I am spinning out, and in general, spinning super-fast is not a good idea on technical terrain (see next point). So, I am often shooting for gearing that skews high relative to optimum seated pedaling cadence.

Second, any time I am pedaling over rough or technical sections, I find I have much better control when I am in a taller gear than I would chose for a similar grade and speed on a smooth section (or on the road). The best advice I got when I started mountain biking that when I came to something technical that I needed to pedal through, shift up a few gears higher than I though I should be in.

If I am on a section of singletrack trail that is really smooth and consistent in grade, and I can keep my cadence consistent, I would guess my cadence is the same as on the road (be it with a road bike or mtb).