Which sounds better 2 way or 3 way speaker design

A 2-1/2 (2.5 way) uses two "lower frequency" "drivers" and an "upper frequency" "driver".

One of the "lower frequency" drivers is allowed to play all the way down to its lower limit and crossed over to the "upper frequency" driver just as a typical 2-way speaker would be crossed-over (or bi-amped).

The other "lower frequency" driver is also played down to its lower limit and is not allowed to play up to the high frequency driver, but rather rolled off at some lower point.

The "upper frequency" driver, is just that.

Any of the drivers can be any of the designs (e.g., cone, horn, Heil, electrostatic, etc.) so long as it can do the job and that has nothing to do with the number of "ways" in the system.  So, at least in theory, if you add a sub to a 2-way, you now have a 2.5-way.

I have two 2.5 ways myself. One is a Super Big Red that uses a Utah aux woofer (the 0.5 way), the Altec 604’s paper cone, and the Altec 604’s integrated horn.

The other is my own creation and uses a JBL 18" woofer (the 0.5-way), a JBL 9.7" woofer, and a Heil AMT.

The JBL 2235 is their contribution to the 2.5-way market.

Ooops, 4435.  Stupid edit time out!

Definitely 3 way !
ALL 2 way have a hole in middle and are compromised ! and my Vintage 40 yr old Allison AL130 ( 3 way w/ push pull twin 8" woofers and the unique CONVEX mids and tweeters ) not to mention unusual crossover points! = 450Hz and 4,000 HZ ( adroitly bypasses the midrange and voice issue ? ) are vastly superior to MANY modern high-end speakers! ( note they were $1,200-1,500 back in day so about $ $11,200 today! defo "high end " speakers if sold today!
too bad so sad noone can make the unique and proprietary and nearly IMPOSSIBLE to make tweeters and mids ( they were actually assembled by robots! YES! )
add a couple modern GR research open baffle servo subs or a vented and sealed combo of 2 servo subs your fav brand and you will have near-perfection ( filter to the speakers at 80-90 Hz fr subs so the tower speaker woofers just do low bass ! )

I also vote for a 2.5 way. I disagree with the statement the midrange needs to go to 80Hz since the common definition of midrange frequencies varies from the low end at 250Hz to 500 Hz and then anywhere from 1.2kHz to 4000 Hz or more at the higher end.  

The Wilson-Benesch Vector speakers run the midrange full range, a common feature of a 2.5 way, and design it to acoustically blend with/supplement the woofer, which is low-passed at 500Hz, and then hand off to the tweeter which is high-passed at 5000Hz. Both crossovers utilize a first order  design. All of these components are designed and manufactured  in house so there is exquisite control over the product. 

Thus, a single driver covers the entire midrange. There are many other excellent ways to preserve the integrity of the midrange, but this one works well and is elegant in its simplicity.

I said ~80 Hz for the bottom of the midrange because the idea is to keep at least the fundamentals of the human voice within one driver and there are those who can certainly sing lower than that.