From my perspective, there is not much difference in fan vs. prop for AEW. It has everything to do with the type of radar aboard the AEW aircraft, and then what that radar requires from the aircraft platform itself.
Take two of the most numerous AEW aircraft types, the E-2 Hawkeye (prop) and the E-3 Sentry (fan). The primary users for these are the USN and USAF respectively.
IIRC the cruising altitude for the Hawkeye is 40,000 ft, about 1,000 ft higher than for the Sentry. In both cases, roto-domes are used, projecting the radar signals above the wings and therefore away from the engines. This needs to occur because the materials of the wing would reflect that signal, and depending on signal output, the radar could negatively impact the safe operation of the aircraft.
This has been part of what has delayed the appearance of the (E-7 IIRC?) Wedgetail AEW&C in RAAF service. The power output from the MESA can impact commands from the cockpit, and therefore the steerable beams need to be programmed so as to prevent them from coming in contact with the wings, etc.
From my perspective, what should really matter is how appropriate an aircraft is in terms of altitude, power generation and loiter time, relative to the radar/comms systems used for AEW.
If the aircraft can fly very high and therefore has a long radar horizon, but the radar system itself is quite short-ranged before the signal attenuates to uselessness, then the aircraft is likely 'overkill'. OTOH, it the radar system can handle long-ranged signalling, but the aircraft can only meet 70% of the power generation or cooling requirements, then the aircraft is likely insufficient.
Similarly, if the aircraft has the 'right' altitude and power capabilities, but can only stay on station for 30 minutes... It would still be the wrong aircraft.
-Cheers