to nayka: your question is very general so limiting the discussion to a vertical Flanged motor with or without feet, there are three commom types of vertical, AC induction motors:
1. Normal Thrust. These motors are essentially horizontal motors with flanges ( usually without feet). The commom industrial flanges in the USA are P, C, D flanges. C&D are usually for machines and fans and P is for pumps. The rest of the world uses metric or DIN flanges.
The efficiency of these motors are the same as horizontal. They are flange mounted, vertical or horizontal, for convenience - usually lower cost.
Note: P-flanges are almost always vertical, D-flanges are usually horizontal and C-flanges, whatever. Larger P-flange motors cannot be mounted horizontally without additional frame support.
2. Medium (In-Line) Thrust. These motors are usually used for in-line liquid transfer. The flange mounted pumps are in-line or part of the piping system. The larger thrust bearings make the motors have lower efficiency - all else equal. The frame has a LP or HP suffix, i.e 365LP.
3. High Thrust. This is the vertical, hollowshaft motor designed for deep well, turbine pumps. These motors have bearings suitable to handle pump thrust and the weight of the pump and deep well shafting. Axial thrust can be up to 100,000 pounds. These bearings have very high losses and the motor efficiency is lower than standard horizontal motor. The actual motor efficiency, sans bearings, is the same as a horizontal motor, however.
Originally, vertical pumps were driven with a horizontal motor with a 1/4 turn belt, which you can imagine was a high maintenance installation. The VHS motor was developed to provide a more robust and reliable installation. At the same time the pump thrust bearing was taken from the pump and put on top of the motor to allow easy replacement without having to pull the pump - a very expensive proposition. This was done by having the pump headshaft come through the motor shaft (i.e. hollowshaft) and couple at the top of the motor.
This motor is common in the USA. In the rest of the world the normal thrust motor is used and the thrust bearing is still in the pump.