Which sounds better 2 way or 3 way speaker design

I would vote for a 2 and a half way....

Both have their own benefits and drawbacks. First, let's assume they are equally well designed. A two-way design tend to make it easier to integrate the two elements into a single sonic "picture" especially at shorter listening distances. A 3-way design tend to reduce distortion as each element is required to cover a smaller frequency span, but also making it more difficult to get them to "gel" into a single sonic "picture", Many times, a 3-way design will require more of a listening distance to get the 3 elements to blend.

Basically, select the one that fits your room and listening distance the best. 

Of course 3-ways would be bigger than 2.5-ways which should obviously be bigger than 2-ways..., right???

These Super Big Red 2.5-ways are only 15.5 cu ft. Those are Chartwell LS3/5A 2-ways on the floor for comparison.

Dear @kjl1065   : Everything the same 3-way is a superior MUSIC reproduction where a 2-way ( almost any. ) has a way higher Intermodulation Distortions that per sé goes against MUSIC in front of the 3-way design.

Regards and enjoy the MUSIC NOT DISTORTIONS,

R.

Am I correct to assume that a 3 way design will give the listener a much better chance to hear the full audio spectrum as opposed to a 2 way design?

Depends on what you mean when you say, full audio spectrum.

If full audio spectrum to you means more prominent low frequencies, than in my opinion I think you would have a better chance of achieving that with a 3-way design, though not necessarily a much better chance. As far as the speakers you have listed, the cello should have 3 db more low end output due to it having two dedicated low frequency drivers, at volume levels approximately 83 db or less (measured at 1K Hz) depending on the dynamic range of your source material and many other factors.

But with any real world test, the proof is in the pudding, so the only way to really know is to do an actual listening comparison.