Which sounds better 2 way or 3 way speaker design

I agree with freediver

"IMO the 3 way floor standing speakers I’ve owned have all sounded more coherent,with better bass & superior mid range performance thanks to the dedicated mid driver".

about better mid, but keep in mind the typical larger woofer which does what the IRON LAW says must be done for bass: move more air!

I want to add, the 3 models you mentioned are all limited by the too common 6-1/2" driver, used alone or in multiples, long throw versions designed to MMA.

Larger magnets not only move the cone, they do a better job stopping/controlling the cone.

I encourage you to look for 3 way designs with larger woofers, keep an eye on higher efficiency/sensitivity, avoid too low impedance dips or designs, consider horn tweeter horn mid,

ports, none, or, if any, front facing, optional port plug is good, especially if rear port.

It depends on the design. There are pros and cons with each, but there are a lot of outstanding 2-way speakers.  They're simpler and can typically offer higher quality parts because there’s simply fewer of them to buy. Because of they can be built for less, many are indeed marketed to the more affordable price ranges, but a TOTL 2-way can still be amazing, depending on the recipe used.  

With that said, there are a lot of great sounding 3-way + speakers out there too. Keep an open mind, buy what you like, and what works in your room on your system, and you won’t go wrong.

"Dedicated midrange driver" is typically an oxymoron and very few three-way systems will not put some of the midrange in the woofer and/or tweeter.  You would need to run the driver from ~80Hz-~4kHz for it truly to be "dedicated" to the midrange.

@toddalin , I always am interested in your perspective.  After reading your above post, how would you answer the OP's question?  

Also, if one was  going to go with a two way speaker, is there a sonic advantage in a two way that is built into its own floor standing cabinet versus a two way that is intended to be placed on a speaker stand?

I prefer 2 way stand-mounts with specific OE stands that are designed for use with the specific 2 way transducer. 

I have 2.5 way floor standers and they sound nice bust not as clear, detailed or have the depth or breadth of my 2 ways. 

Now there are many variables that play into this also, room size, room treatments and so forth.