Which sounds better 2 way or 3 way speaker design

As has been alluded to, it's all about the design.  Most specifically the crossover (assuming you have high quality drivers).  It's easier to get a 2-way design to have proper phase characteristics between the tweeter and woofer/mid woofer.  the coherency of a great 2-way design can be quite beguiling.  To get a 3-way design to sound coherent from top to bottom (highest frequencies to lowest frequencies), and to speak with one voice requires, requires some very intelligent crossover design.  With a 3-way you now have two crossover points which need to be optimized.  Optimizing the phase and frequency balance at both crossover points to allow drivers, on either side of the crossover points, to work in harmony should be the aim of a great design.  When it's done right, it's fantastic.  And the benefits of multi-way designs are now fully appreciated (greater extension at both extremes, lower distortion, greater dynamics, more power handling, etc.).

Dear @knotscott  : I agree that always exist trade-offs .

Now, a woofer in a 2-way design usually crossover around 2khz and the most critical frequencies are handled by that woofer and it's here where is developed that high IMD due that that woofer handled  from around 40hz and up and that developed IMD puts a lot of " dust " in the midrange and in the HF because we have to remember that everywhere are developed harmonics that starts in the bass range.

R.

Then there's a 2-way pair with a sub that can cure or complicate where and how driven and the dispersal of said.....a 3-way with sub would seem to live better in a larger space....

It can as well to consider the thoughts to the size of the various drivers applied, 2 or 3 x sub size.....

...an that's why I like a good equalizer, even if the speakers have on-board adjustments for the x-overs...

My approach, a  IMH....*s*

3 way designs are more difficult to get right. Also 3 ways are more expensive, so be suspect of a 2 and 3 way design of similar price.

It would seem crossover design is really important to a three-way. I guess if one was to ask this question with the assumption that if you had a three-way versus two way which would be better assuming crossover designs are not part of the evaluation process because they are assumed perfect for each situation.

It would seem to me if this was the case the three-way would be advantageous.

And of course assuming driver and cabinet designs are not impacting the decision either. I think it’s a theoretical question and to me if you separate out the mid range and not have it intermingle with other spectrums that may offer interference it would be better to have a third segment of frequency range and create a situation where more detail is better.