Pro's
1. Less drag, smoother airflow through the inside of the airplane than a non-ducted installation.
2. Cleaner install (if done properly)
3. Less chance of equipment inside the plane coming into contact with the turbine (either fod in the intake, or melting onto the side of the case).
4. More protection for the turbine in a crash
5. Might also help avoid having fuel spray come in contact with hot engine parts in some crashes (less chance of a fire)
6. Easier for inexperienced builders to set up a bypass system that is pre-engineered without making mistakes.

Con's
1. More difficult turbine access.
2. Much more difficult to scratch build using a bypass because the ducting and fuel tanks need to be designed and built to fit the airplane.
3. After engine shutdown the radiant heat from the turbine will be contained inside the bypass, necessitating the use of a fan to help with cooling (yes I realize this is a good idea even if you don't run a bypass, but it is pretty much mandatory with one).
4. Takes up more space inside the airplane.
5. Higher cost.
6. Some propane start turbines are more likely to "BANG" on startup inside a bypass (usually doesn't hurt anything, but it gets everyone's attention).

I'm sure there are more on both sides...