Others mentioned the big benefit of the three piece is that you can easily connect a blowoff tube. The downside is that they tend to have way more suckback than the S airlock and evaporate quicker.
I tend to use the three piece airlocks I have on some of my smaller fermenters for primary because there's less headspace and more chance I need a blowoff. S airlocks for everything else. Anything aging for a while has an S airlock to avoid problems with suckback and evaporation.