For a single stage ANSI B73.1 pump, the hydraulics will be identical as Tim has stated. Vertical pumps will have a lower installed cost because of the lesser foundation requirements, and they take up a lot less space. However, from a reliability standpoint, the vertical pumps tend to have higher vibration levels and more seal problems (unless using an expensive double mechanical seal). Beware that vertical pumps are available either with a rigid coupling and no bearings, so that the impeller is cantilevered off the motor shaft, or with a normal power frame and flexible coupling between motor and pump. The bearingless type with rigid coupling is cheaper, but far inferior in vibration levels and seal life. Either type of vertical is hard on seals because of the tendancy for the seal to run in a vapor pocket rather than liquid flooded.
If its not already obvious, I don't like vertical pumps. From a reliability standpoint, assuming all 3 are installed properly, my preferences would be, in descending order:
1.) Horizontal ANSI
2.) Vertical ANSI w/bearings and flex. coupling
3.) Vertical ANSI w/o bearings and rigid coupling - NOT RECOMMENDED