OKW has a tiny bar, but you can take your drinks outside to sit and enjoy them.
I am less familiar with AKL (haven't stayed there yet), but I am certain they have at least one - along the lines of the ones offered at the other deluxe resorts.
AKL has Victoria Falls which is upstairs from Boma. It's small, very dark and noisy (from Boma) plus it's often full of people who are not getting anything to drink but taking a table/seating while waiting for the dining buzzer to go off.