Which sounds better 2 way or 3 way speaker design

I’m partial to my 2.5-ways. They use a JBL 18", a JBL 9.7", and a modified Heil. (BTW, a Heil is equivalent to 8 square inches of tweeter surface.) And these do keep the midrange in the 9.7 going all the way up to ~3,500Hz before crossing over to the Heils. This maintains coherency, staging, and imaging. I really don’t fret about a wide dispersion as I always sit in the sweet spot, and a narrower dispersion results in less wall bounce for better staging and imaging.

So lest someone think fewer ways means less cone area, think again. Some of the biggest speakers are 2-ways.

Actually, the Heil is 29.76 square inches of tweeter surface.  I was too late on my edit. 

I am under the impression, (which I may be incorrect) that a three way design is superior to a 2 way design.  
 

Wrong - it’s the quality of the parts and implementation.  Some crossovers are done extremely well they seem seamless.   More crossovers “may” offer more opportunities to have a poor crossover, but it’s not automatic.

As usual, best to demo yourself to hear what resonates with you.

Ime loudspeaker design is a fascinating competition of ideas, every one of which is a juggling of tradeoffs (and anyone who tells you otherwise is in marketing). The implementation of those ideas can take very different forms: Single driver, two-way, three-way, four-way, planars, horns, multidirectionals, omnis... And even among speakers which are outwardly similar, the designers are constrained to giving some attributes higher priority than others.

In general the attributes which I prioritize are more likely to be found in a conventional three-way than in a conventional two-way, but my own designs tend to be unconventional two-ways with rear-firing tweeters, often augmented by subs... in which case I guess they are three-way systems?

Duke

One of my favorite basic design is a three-way, with a compression-driver/horn midrange covering a wide part of the range.  The compression drivers I like are all vintage—from 1930’s to 1960’s.  I own a system fitting that description—twin 12” woofers (modern), bullet tweeter (modern), western Electric 713b midrange compression drivers (1940’s), Western Electric KS 12025 multicellular horn.

I mentioned two single driver speaker companies I like-Charney and Songer—above, and I would now like to give kudos to PureAudioProject which makes terrific open-baffle speakers, modt of them are two-way speakers.  

There are good speakers of all types.