Well, I'd go for the cylinder, because once it's spinning evenly there is no upward or downward forces on the water at the edges (the edge of a vortex in a cone or hemisphere will want to rise up the cone or hemisphere in order to rotate with greater diameter). This means firstly that friction with the sides is contained and does not "pollute" the central column, and secondly that there are no Guinness-bubble-like vertical circulations dissipating even more energy.

That is completely made up as I went along, though. I suspect this is actually a very nontrivial problem, not actually amenable to analytic solution. (Unless performed in very maths-ised physics, e.g. frictionless container in zero gravity.)

Peter