I'm certainly no authority, but I have made a handful of two-piece bows. I believe people who have made them are very comfortable with them. Shooting quality will be what ever you want it to be. They're more portable, store more easily, and a slip up in construction typically only costs you the price and work of 1/2 a bow. Mike Yancy encouraged me into two-piece bows sometime ago and I've never regretted any of the pieces. Also, it's typically not as hard to find a nice 3' piece of material with just the right shape as opposed to 6' of straight wood.
I'm curious to hear how the others reply, but I think the indexing of the handles might be intimidating for some-it was probably one of my bigger hang-ups. Also, I somehow felt that the take-down apparatus was kind of a "gimmick", and made my bow less traditional. However, if you research the literature, they've been around for a long time, well back into the 1800's. Fred Bear spent a great deal of energy and resources developing take-down hardware, and I believe pattened more than one device. I think when a bowyer creates the first, they're a believer. My son is just finishing up on his first, but he wouldn't touch one until he saw that mine have been good, solid, hard-hitting bows. He was very cautious to keep the center of the backs lined up, and his current project will probably shoot as well as any of mine.