Which sounds better 2 way or 3 way speaker design

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.
 

Having owned Proac speakers in the past I would not rule out the K3 without having an audition. Unfortunately my listening room will not accommodate them but .....

A great discussion.  I’ve had so many speakers over the years from single element to 4-way in many different rooms including large towers and smaller bookshelves.  I agree with the comments that stress design and execution including component and build quality.   My old friend that was involved in speaker design and build always said there is no perfect speaker and that there were trade-offs in any design and build.  I find a key is the room you are listening in and what sounds good to you at this time.  I now listen in a relatively small room so small towers or 2-way bookshelves fill the room better without overpowering the space.  In addition my old man ears don’t hear as high in range as I used to so sibilance is key as as such there are speakers I liked when I was younger that I wouldn’t listen to now.  Trust your ears and what sounds good to you in your listening room.  I haven’t had those 3 speakers but With an 18K budget you’ve got some great choices.  

Over the last 2 years I’ve been on the Speaker Merry Go Round going through 11 sets of speakers… Yep 2ways, 3ways, and Maggi’s and opted for stand mounts with dual subs… YOU REALLY NEED TO HEAR THEM IN YOUR ROOM TO BE SURE… I can tell you the Triangles I tried had a very short life in my room. I have to say every speaker I tried had a great honeymoon period but once the crucial listen began, 10 of the 11 speakers were asked to leave.

I ended up with Soundfield Audio MMW1’s, Custom designed for my room’s shortcomings and my listening tastes. I met the designer / owner of Soundfield (AJ) at the Florida Int’l Hi Fi Expo in Tampa and his room’s sound blew me away. It’s been nothing but sonic bliss since. There’s several Soundfield Youtube Videos on line, one where the Audiophile Junkie claims Soundfield Audio is the best small room option out there…check ‘em out.
Which ever way you go, LOOK WITH YOUR EARS, not that my speaker has more speakers than yours, LOTS OF GOOD OPTIONS OUT THERE with excellent Build Quality & Component Quality.