APU running and fuel weight / landing speed
One fact about this incident that I learned from the 60 Minutes report this past Sunday is that they got the APU running. Sully mentioned starting the APU as one of the first steps he took following loss of power. The RAT may have deployed, but they also had APU power so continued flight control was possible and gear extension would have been possible if they had tried for a dry landing.
As to the discussion of empty vs. full tanks one related factor is touchdown speed. Sully mentioned that he was trying to manage speed for the slowest possible touchdown without excessive pitch attitude. It is of course an academic discussion, but if the fuel load were less, the overall gross weight would have been less and he could have further reduced speed prior to touchdown. The aft cabin crew member reported a rather violent touchdown during which she was injured. Had the airplane been lighter weight, landed slower, and thus landed softer she might have been better able to prevent a passenger from opening one of the rear doors. Although she tried to close it that proved impossible with water pouring in. That door being open caused the airplane to sink much faster than it would have otherwise. Fortunately it stayed afloat long enough.