The stepper motor has more accurate speed control, which may be refined to an angle of the stepper motor rotor position. This means that the motor speed may be control within one motor rotor revolution. The DC motor does not have this capability. Stepper motor then requires somewhat different controls for the precise speed and the rotor angular position controls.
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DC brush motors have been very successful for the fact that they have very smooth velocity regulation and low speeds. The disadvantage is the construction of it...and brushes wear out. Now steppers too have good velocity regulation. Because of the design, they are either running the speed you told them or the are not running at all. Problems with stepper system are that there is a velocity ripple that is noticable due to the stepping. Stepper also do not like slow speeds (<1 rps).
It also really depends on the stepper system. Some of today's stepper drives are really amazing. With all of the micro-stepping technology and anti-resonance technology, steppers are doing amazing things that they could never do before. Check out IDC Motion's SmartStep & Impulse. Also check out Oriental's AlphaStep. Compumotor & others also have systems, but pry not as advanced as IDC & Oriental