2-piece bats IMO are now very popular (Demarini,Easton) and seem to be here to stay.They say the major benefit of a 2-piece bat is that it gives more flex to the barrel at the point of contact and, therefore, increases the "trampoline effect". Look at what the majority of all college players are using,they are using 2-piece bats.
1-piece bats IMO are stiffer and have less "trampoline effect"
My DD has two composite bats that she uses. The 2-piece design the ball seems to jump off her bat much more than the 1-piece.
In the end it comes down to what your DD feels more comfortable with.
Two piece construction allows for a more economical way to vary the stiffness of the handle and the barrel, and this increases performance because flex can be put where needed and stiffness elsewhere. The two pieces also help negate some "sting". In the past, some two piece bats have suffered quality issues but I think this has been addressed the last few years.