Which sounds better 2 way or 3 way speaker design

I really like the designs with no midrange crossover but they are somewhat output limited. Again much easier to make a good 2 way which should have better time and phase characteristics. A dedicated midrange driver is both a blessing and a curse due to the crossover. Never could warm to the original Heil driver.  

A major variable is your room size.  Putting a 3-way loudspeaker system in a small room would be fraught with many room interaction issues. A 2-way will mitigate these issues. 

mofojo is pretty spot on.

I'm using a 2 way with a sub that integrates perfectly with outstanding results and a 3-way in my room would be overkill.

Good hunting

After much experience with many speakers (mine, audiophile friends, and at our local high end store) my conclusion is that under around the $10k price point a 2 way with a powered subwoofer (2.2 setup) is the best sound. 
 

under around $10k price level 3 way speaker cabinets are not stiff enough for the bass driver and the midrange and tweeter suffer because they are vibrating along with the cabinet. Careful listening brings this out and with noticeable but subtle lower clarity. 

Stop counting and just listen. 

The. answer is 2 ways + a sub so how many ways is that?

@rwwear wrote:

Don’t dismiss 4 ways.

+1

There are different approaches to a 4-way (or any other -way) design, of course, but as I have outlined earlier I prefer what’s essentially an augmented, high efficiency 2-way system based on a large format horn/compression driver crossed over to a 15" direct radiating woofer (or two of them) in the 600-650Hz region (horn-loading is arguably even better here, but its upper end range is limited and thus creates new challenges for the mids/tweeter meeting it). Large pro woofers provide critical displacement area, high motor force and headroom in the important power region while having limited dispersion (and excursion) due to their cone size, and coupled to a large, fitting horn/CD will match the directivity pattern at the XO (where the horn will still control directivity) for good power response here and a much smoother perceived transition. Also important is that a large, 2" exit horn/CD provides for much better energy and physicality its lower region crossing over to the woofers compared to smaller exit horns, which is why the midrange from such a large format horn/CD + woofer(s) combo truly excels in most every parameter with its coherent, unforced, and uncluttered clarity and presence. Well implemented, think the 3" ATC midrange dome or larger panel speakers on steroids.

Such a 2-way design, depending on the specific 2" exit compression driver with its 3 or 4" voice coil/diaphragm, will typically need augmentation in the upper octave, but fortunately blending in a dedicated, high eff. super tweeter at or slightly above 10kHz isn’t a critical XO-region - what matters is integrating such tweeters properly. Same goes with the lower end of the woofer section; high-passed in the 80-100Hz region and augmented with subs they’re virtually freed og LF and visible cone excursion and will perform even better (with 6-10dB more headroom) from the upper bass on up, not to mention match the horn section above more seamlessly. If configured actively the best integration can be had with elaborate delay settings etc.

Choosing or having the crossover region(s) more or less chosen, depending on ones design preference, is a compromise in every variation. The challenge is how to work around them and take advantage of a given approach and the drivers/horns used. A driver covering the entire midrange fundamentals from LF on up in an unassisted 2-way system is a good outset, at least in theory and a limited practical context, but the woofer/midrange used will need to be fairly small (i.e.: 6-8") to extend high enough in its upper range, and this again presents challenges (not to mention being counterproductive) for its abilities into LF territory, in addition to IMD and Doppler distortion acting both as a non-highpassed woofer and midrange. Neither the woofer/mids or typical 1" direct radiating dome tweeter can be expected to perform their best in the upper and lower end respectively, macro dynamics are limited and headroom is more or less nonexistent. I’ve heard quite a few very good such 2-way speakers though, and in smaller to moderate spacings at no more than moderate SPL’s can be fine performers. A friend of mine is using a pair of great sounding and subs augmented Stage Accompany M57 speakers with dual 12" high eff. woofers and a high eff. ribbon type midrange/tweeter in an MTM config. crossed at 1.5kHz, all actively. So, 2-way main speakers as well (i.e.: a 3-way system w/subs), but very different to the previous, low eff. 2-way solution mentioned for a variety of reasons. A high eff. 12" woofer can be an excellent central to lower midrange driver, but exhibits more "character" in its upper range compared to a 2" exit large horn/CD solution (that I use) in the same region, which is audible in particular with piano and the lower range of violin. Conversely the ribbon driver extends higher than the large horn combo, which then needs super tweeter assistance for what amounts to a 4-way system in total (also subs-augmented). And on it goes; different solutions, different strengths/challenges.