I shoot mainly 3 piece takedown recurves. I like the extra mass. The only downside I can see is the noise that occurs in some bows in the limb connection. I have tried to eliminate that noise with Teflon tape, padding between the limb and the riser, etc., with mixed success. It seems to be luck of the draw, some bows have noisy limb connections, some don't.
I have two two-piece bows: a Robertson Wolfer recurve and a Robertson Vision longbow. The Wolfer has a bow bolt and the Vision has a hinge. Neither bow has any noticeable noise from the connection, and most people wouldn't notice they are two piece bows without being told. They are both hunting bows, and would be difficult to transport if they were one-piece.
I also have several one-piece bows (including a one-piece Schafer longbow, Bowwild). These are either bows I don't intend to transport other than locally, or bows such as Classic Bear Kodiaks where one-piece is an inherent part of the look.