Two way vs. Three way Speakers

A simple 2-way with really good drivers and crossover put in a properly designed box can be absolutely stellar.  As stanwal menionted, you're most likely to give up deep bass from a good 2-way, because anything larger than an 8" woofer tends to cause other issues.  Bass output is relative to the room, and can always be augmented by a subwoofer (or two). 

A 2-way is simpler to design, and less costly to buy good parts for, so when shopping at a price point that's worth keeping in mind, but it really depends on what you're preferences are and what the specific speakers are.  I'd personally rather buy a well made smaller 2-way to get stellar mids and highs, then add a sub if necessary, than to give up that critical clarity permanently just so I get more bass output from a larger 3-way.  Just my preference. 

Like virtually any engineered product, there are an endless series of tradeoff decisions to make when designing a speaker and deciding on 2-way versus 3-way (or more!)  As others have noted, transitioning from one driver to another affects the sound quality in that frequency range.  The ear is particularly sensitive in the bandwidth in which most instruments (including voice) have their fundamental range -- roughly just under 100 Hz up to about 3,500 Hz. Some speaker manufacturers try to avoid switching drivers in this range.  However, if you try to use a large driver (to preserve bass) you'll end up with beaming in the upper range of this band. Using a smaller driver addresses this issue, but makes bass response more difficult. 

And these trade-offs go on and on in lots of other areas. Ultimately, all you can do is audition lots of speakers and see which make and model best lines up with your own preferences. 

Or, you could do what I did and end up with a set of Ohms. They use one driver for bass up to around 8 kHz and only cross over to a tweeter at that frequency. But, they have their own compromises since they have a semi-omni radiation pattern, which some love and others don't.  

So, the advice you get here may give you some interesting candidates to check out but ultimately you should ignore the rigid advice others give and just buy what sounds good to you. 

I have three systems. One has two-way speakers. The other two have three-way speakers. They all sound good.

It does not matter if it a 2 or 3 way speaker. It is all about frequency range and even dispersion without the driver breaking up. Driver size plays into dispersion so this is often why speakers are 3 ways too. Both designs can work well.

I currently use a 2 way (JBL 4367) and my last speaker was a 3 way (Revel 228be) and those designs could not be more different but both had about the same frequency response in my room. The revel hands off to the next driver to keep dispersion wide and distortion low. The JBL uses a horn to let the “tweeter” play lower than it normally could. The results are about the same…. But the JBL is a lot better but that is a discussion for another day.