2.5 or 3 way; why one over the other?

Not all 2.5 ways have identical woofer/mids by the way.

Focal Profile 918's used two 6" drivers in a 2.5 way crossover but the top woofer had a smaller voice coil and had better high frequency extension. 

I disagree that 2.5 way speakers are designed because they are cheaper. I think they are good engineering trade-offs for a lot of rooms. 

@yogiboy 

In a 3-way the midrange has 2 filter sections. A high pass, and a low pass. 

In the case of a 2.5 way, the "midrange" is missing the high pass filter. 

That is exactly how you define the 2.5 way speaker system. 

The woofer and tweeter filters are otherwise the same in either. 

I'm not sure about Focal's current line up, but the Focal Profile 918's were an example of a 2.5 way. 

@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. 

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.