Fixing a stepper motor by its shaft

Are the two schemes equivalent?

Mostly so. Usually the motor is affixed to a sturdy chassis resting on a solid surface, sinking vast majority of vibrations and jerk coming from the motion. In your configuration, both the motor and anything attached to it will be fully exposed to these vibrations - which introduce all kinds of headaches like electric connectors losing contact, wear of joints from material fatigue, screws coming loose, and so on and so forth - not a single thing critical, just a mountain of small headaches. You're also dealing with accelerations in case the element turns fast (and especially if it stops rapidly, say, knocking against a brake), and you have to get power and control to the rotating part somehow. Control is fairly easy using short-range wireless communication like bluetooth or IRDA. Power is worse - you'll either limit your angle so that an attached cable doesn't get too twisted, or supply power through batteries. Or you can use a slip-ring for both power and data, but slip-rings are another can of worms, something that works okay in 'big industrial', but on small scale is so fault-prone and quirky you're better off redesigning everything to have a fixed stepper.