Two way vs. Three way Speakers

In terms of sound what are the differences good and bad between two way and three way speakers. I have been researching and collecting information about a diy speaker project - for example looking at the SEAS Thor design (three way) vs something like the Proac 2.5 clone which is a two way. Still reading about other options too. Best speaker I ever owned was Maggies through the 80's that sadly were not child friendly. Currently have 2 way - Paradigm monitor. Looking for accuracy, detail, clean sound (great mids and highs)that is true to recordings - for cds through modded Jolida (warmer) and MF amp. Thanks for any discussion and thoughts on this.