I like them all for the most part anyway.
The mass is nice in the 3pc. Lots of grip and riser shapes. You can have LB and recurve limbs with some boyers or with ILF. Then there is all that extra great looking wood you can fit in the bow.
I really never brake down the 3 pc unless I am heavily packed with stuff and going to be doing a lot of traveling before I need the bow. It just takes too long to take apart and assemble to do it if you don't really have to do it. When I take it down, it gets very compact.
Most 3 pc bows have short site windows in the length of bow I want to shoot. That can be the big down side for some people. I have done some form changes and find the shorter site window on most 3 pc bows now put the corner of the top limb in my site line when I shoot split finger.
The shallower cut depth, usually longer angled site window, and narrow riser and limbs on most 1 pc LB’s give much less visual obstruction with minimum canting. I am back to the one piece as my preference unless I make a permanent change to 3 under so I can work with a shorter site window.
I don't like the long one piece for travel. I find it hard to pack them longer than 62" in my current vehicle. Most times I can live with it, but sometimes it is a pain to travel with a longer bow.
Now I am looking for a 2 piece more and more, but those have their downsides. I can't get some of the bows I like in a 2pc of any kind. Used ones are rare and the right length and weight. I like the little extra weight of one. I like the sleeve for strength, but I don't have big hands so some of the sleeve grips are a little big. I can't get some of the grip shapes I like in a sleeve. I like leather grip wrapped grips. Some people don’t and you have to have some kind of grip cover with a sleeve. I am looking at bow bolts, but I still can’t get every bow I like in a bow bolt. I also don’t trust them without phenolic in the riser and that means very little room for nice wood in a riser. You spend a lot more for a 2 pc than 1pc. In many cases more than a 3 pc.