Which sounds better 2 way or 3 way speaker design

Implementation is everything.

However, while designing a new speaker, choosing a 3-way may remove a number of constraints a similar 2-way would have, related to distortion and dispersion and dynamic range.  I wrote more about this here.

Having said all of that, trying to judge 2-way speaker A vs. 3-way speaker B is a fool’s errand.

We can start to think about the benefits along the same lines of "why use 2 drivers instead of just one?" Similar benefits will appear when asking "why use 3 drivers instead of just 2?"

It is of course possible to go overboard and design a multi-way monstrosity that sounds horrible.

@rauliruegas

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.

There’s never a free lunch. You stated a potential benefit from choosing a 3-way design, but there’s a flip side.

A 3-way system typically puts a crossover point (a series capacitor) in the 300-800hz region, and it induces any associated delay and degradation from the capacitor. That’s right square in the middle of the vocal range, which covers the primary music range of a lot of instruments. All things the being the same, that’s most definitely a theoretical disadvantage to at least some aspects of the sound.

Every speaker designer faces lots of those choices. Dealing with all those pros and cons, is simply a matter of picking your poison, and mitigating it as much as possible, but no design is immune.

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*