Which sounds better 2 way or 3 way speaker design

I have no knowledge of the three speakers in question.

Whether a 2 or 3 (or 2.5 or other) way is best is dependent on the selected components, construction, and it’s implementation. There are fine speakers made in many "ways" and I don’t think that the actual number of drivers is the important factor in deciding which to choose.

In general, I would think that a floor standing speaker would offer more cabinet volume and this would typically allow for a deeper, more generous bass. But of course there are exceptions to everything.

A 4 way and don't look back! 

I've upgraded through the Usher line over the years. Started with BE-718s then Mini One Diamond, then Mini Two Diamond. I prefer the fuller mid bass and the richer sound of a larger output speaker design.

Incorrect question, All depend of design, drivers, crossovers etc 

3 is larger than 2. (until our mighty leaders will change the rules ,at least)

So why would a 3 way not be better? Why would they bother with 3 way?

I think in small spaces you may not benefit from 3-way design, but overall, sure, 3 way should be better, when it's not a cheap 3 way vs a quality 2 way..

I don't know what you mean by full audio spectrum? I would go with the Totem from these three, based on the data. Not that I know anything about speakers in 18K price range