I was in the same dilemma a year ago and decided for Park Hyatt. The Virtuoso benefits were great, and we liked the central location where one can leave the hotel and walk around. The area (Beyoglu) is rather chic and there are plenty of shops, bars, cafès and restaurants. Also, getting to Sultanhamet was fairly easy, as traffic was not too bad (not as bad as on the waterside road leading to Besiktas and FS Bosphorus which was jammed up all the time).
For a regular city trip and sightseeing => PH
For a special, romantic getaway => FS (preferably in a Palace room, but these are really expensive...)