The best thing to do is to listen to the speakers before you buy them. Good stores will usually have a setup where you can send em through an amp and listen to them with the tough of buttons (like Best Buy). Try before you buy man! You might not like the speakers if you never listened to them first.
However, if you can't listen to them, three-way is significantly better than a 2 in my opinion! Each speaker plays a role of attacking a certian frequency. What you want to look for on a speaker is a flat mid and high-end frequency response, and the 3-way is much better at achieving that. Each of the three speakers cover a certian frequency range, dedicating a certian range of sound per speaker.
This is a graph of the response of an anonymous speaker. The blue line shows a fair response while the red one shows a pretty poor one. A flatter response will result in clear mids and crisp highs without hearing that "piercing" sound when played loud.
Hope this helps!