2.5 or 3 way; why one over the other?

Width and sensitivity are two attributes that come to mind.

2.5 ways are often narrower, deeper than a 2 -way, but also have more output per volt.

In some ways I think they are the ideal apartment dweller’s speaker.

The extra woofer helps overcome the "baffle step compensation" issue, but they do tend to have a little lower impedance as well. 

Unless you really need to go very low and play your music very loud, large scale music at near concert level, great 2 way floorstanders that do 30hz well is all that's needed for a medium size room. One tweeter and 8" woofer. And great source and electronics. And wall current and cables. Speakers should be as simple as possible in terms of parts and wires. Building cabinets and tuning speakers is a different matter.
Can't answer your question, though, your ears should tell you which ones to get.

https://forum.audiogon.com/discussions/is-the-2-5-way-speaker-the-ideal-home-speaker

@larstusor

With a 2.5 speaker the woofer and mid range are the same size. With a three way speaker the woofer and mid range are a different size. They both have two crossovers. I have owned Spendor 2.5 way speakers and they were outstanding. From what I gather that is the difference between the two types!

@yogiboy 

A 2.5 way is missing 1 filter section. The "mid" has no high pass filter. 

Typically, the two woofers are the same, but Focal and possibly others, have used slightly different models.