Geeky reply
I've had this debate with guys who've flown both - but there's good reasons why props and jets are used, each having strengths and weaknesses.
Jets:
-Allow higher transit altitudes and better fuel consumption/transit time, better endurance at high levels
-Quieter to hydrophones and other equipment subs use
-Modern jets can have better performance so longer runways aren't required - there's developments of a new Boeing airliner into some kind of american equivalnet of the 'Rod
Props:
-Instant power 'bite' if you need to get away from the sea at LL, and can be more easily controlled with prop disk effect, no airbrakes required.
-Endurance at low level is better than a jet
-Relatively efficient compared to the turbojet Spey (part of the reason Newrod is getting turbofans!)
Hope this helps