2-Way 3-Way Debate

I have owned many speakers over the years,and I must say I always preferred two way over three way.

As Mlsstl states, "take your pick."
Crossover points and components involved in the crossovers do affect the sound as do overlap between speakers. Therefore some think simplier is better. However, you will not get true full-range frequency coverage from a single driver, or from most two-ways. When a manufacturer tries to squeeze out a full-range frequency response from a two-way speaker something usually suffers when the midrange driver is asked to cover the top end of it's frequency range or when the tweeter is pressured to extend below it's comfort zone. Even the highly regarded Audio Note AN-E, a rare two-way that is said to operate essentially full range (specified from 18 Hz to 23 kHz at -6 dB; when placed in the room corners) is said to have a "slight cupped-hands coloration," according to John A with Stereophile).
One benefit of small cabinet two-ways is in imaging. Most find imaging to be improved when using a smaller cabinet sized speaker. Some solve the extension problem by adding a sub to a two-way, but this is not ideal as most think two subs (or more) are better. When you start adding subs, the question becomes "wouldn't it be better to simply purchse a full-range speaker?"
Regarding crossover slopes, a few very highly regarded speakers use shallow first-order crossover slopes, such as the outstanding Venture Ultimate Reference reported on in this month's Absolute Sound. However, the majority of manufacturers choose steeper slopes that allow the drivers to operate in their optimal frequency range.
Personally, I would use smaller two-ways in a smaller room, and then add a sub or two since it would be easier to adjust and integrate the bass response when using adjustable subs. I choose to use larger near full-range speakers in a larger room.
Like many things, there is no "right" answer. I would first think about the room size and where you will position the speakers within the room, and second about the amplification you plan to use - high or low power, SET tubes or a 500 wpc SS amp. The amplification (and matching sensitivity) significantly affects the sound of the speakers to the point where you might never hear what the speaker is capable of when powered by a mismatched amplifier. Finally, I would go out and listen (with the type of amp you will be using) since no one design feature will solely determine whether a speaker sounds good or bad.

Split the difference, my speaker crossover design is called a 2.5 way design.

Limiting the conversation to conventional dynamic drivers and not horns...

Let's say the tweeter, as typically, goes down to 1.5 to 2KHz. In a 2-way, that means the woofer has to cover up to that. Any woofer, any size, designed to accommodate that wide range will be compromised for upper midrange or low bass. More the latter. Physics, mass, etc...

Then, you get into power handling, which is also driver and frequency dependant. End result will be that a 3-way is more likely of stronger dynamics.

In a 3-way, you also get to raise the tweeter crossover point, which can be very useful, particularly for some ribbon types. Our ears are most sensitive and discerning in the vocal range, although that exact frequency range is still debateable.

Every crossover has a phase shift but so does the driver, over a wider range. The advantage of 2-ways is not only the simpler design but the higher crossover uses smaller inductors and capacitors.

It comes down to how you listen. A personal choice. Nice to have a choice.

There is no debate... each can be very good, what makes one better than the other is the designer, what parts they choose, crossover points, slopes etc. I have built more than most. I love,love a good 2 way, its easy to achieve great results with a wide array of parts... in 3 ways, I've had the best results keeping the crossover point out of the vocal range, also, there are alot of 4, 5 & 6 inch midbass drivers that can be crossed down near 100 hz and still run fairly flat out to 2 to 3k. This keeps the hard bass off this driver, limits excursion and over working the driver, keeping vocals smooth and accurate as well as giving you a wide variety of tweeters to blend well, you will find that typically (not always) very good 2 ways have the tweeter crossed low... on the 2 way mtm's that I use now, I crossed at 1.7k, with a 3 way you will find countless quality tweeters that can cross at 2.5 to 3k, but even going down to 1.7, your choices narrow by 50 or even more.... For what ever reason, I've had a tougher job finding great matching components in a 3 way.
Even though that I typically prefer 2 ways, on a very well thought out design with good parts, a 3 way should be better, but all in all, parts choice, crossover frequency, sloped etc make all the difference, so its all in the hands of the designer