While the Central Intelligence Agency does a lot of things for this country, and does a lot of those things right, the military is the one who should be conducting drone strikes. That is what their specialty is, and we would be much better served if they were the ones doing it.
I think that if you look back and see how effective the drone strikes have been with the Central Intelligence Agency in charge, then there really is nothing to be gained by turning over control to the military. The CIA has done a fine job, so let them continue their work.
I believe that the CIA should handle the responsibility of the drones. That agency has more access to confidential information than the military and it would seem to me that since drones are meant to take out individuals or precise targets that the CIA may be better suited for that mission.
Drone strikes are (deservingly) becoming a very touchy subject but I don't think a change of hands from the CIA to the military fixes that. The people that don't trust one don't trust the other either and I doubt they'd differentiate in how they used them to any noticeable degree.