I have been passionate about audio equipment, and speakers in particular, for around 20 years. During that time, I have gone through hundreds of written and spoken reviews, tens of listening rooms and, most importantly, I purchased 4 sets of speakers that I am using very actively.
From all that experience, my 1st grand conclusion is that the higher on the audiophile scale you go the less it matters how many drivers your speakers have; provided we are comparing apples-to-apples (i.e. bookshelf to same-size bookshelf).
To continue, I must make some generalization: “high on the audiophile scale” is directly correlated with “high on the price scale”. If we exclude extreme cases, that generalization works well, at least for me. As I have been constrained when it comes to funding the hobby, I had to operate below my personally defined level of “high”.
Based on all I learned, my 2nd grand conclusion is that well designed/built 3-way speakers outperform their well-designed/built 2-way brothers. Again, provided we compare apples-to-apples, and again, when we talk about the speakers below "high" area on the audiophile scale.
I cannot precisely pin-point the reason of the above, but having a mid-range driver makes subtle, but easy to notice advantage. My last purchase (2021) was actually 3-way bookshelf speakers. During my selection process I found 2-way speakers that could deliver the same quality sound. Both sets had nearly-identical parameters, though 3-way was 4” taller, due to the space needed for the mid-ranges. The choice was easy. Because the 3-way were coming from “lesser” brand, their price-tag was around 50% below the 2-way set, manufactured by a well-recognized and well-advertised powerhouse.
To round it up, if you can afford reaching higher on the scale, the 2 or 3 way will not matter. And a side note: I decided not to name the brands/models as my goal is to provide an extra dimension to this, very interesting discussion and help those who are making the call between 2 and 2 way.
Cheers!