Been searching FT and found a dearth of info on Both Doha hotels. I'm in the very same boat as the OP, 36-hour stopover first visit to Doha. Trying to choose between properties, want to do museums and the Souk and dip my toes in the Persian Gulf (which I know is do-able on property at the older one), generally want things convenient for getting around. This will be in early March.
Particularly welcome comments on the IC Club lounges.