perhaps this for starters
A free turbine engine can be designed so the power turbine(s) run at a different speed (RPM) to the compressor stages, thus allowing the engine designer to select the optimum design and speed for both sections of the engine to meet the particular requirement.
(higher propeller rotational speeds and noise level during ground operations?)
A fixed shaft system has longer shaft(s) creating more torsional loads and perhaps needing more bearings.
The starter/generator of a fixed shaft engine must turn over the dead weight and drag of the propeller so presumably is more robust, heavier, have a bigger current draw (perhaps requiring a longer recovery period for the battery before starting #2).
etc
regards