The advantage of the free power turbine is that it is simpler than a fixed turbine as there is no mechanical link between the gas turbine and the gearbox. The downside is that it has to 'windmill' in the exhaust flow thus losing a little bit of available power in the process.
The fixed turbine does as Silvio says need a clutch system which complicates things slightly.
Most free power turbine helicopters that I have flown have been twin engine helos and therefore needed an Accesory drive system to allow one engine to power the ancillaries whilst the second engine brings the rotors up to speed.
As to a direct 'engineering' advantage I'm afraid I couldn't tell you factually. Ask Nick Lappos who could give you the techie answer.
