I have had Dermabrasion, but never Microdermabrasion.
Dermabrasion is done by a plastic surgeon, in a hospital. The recovery time is months.
The procedure is used on patients with severe acne scars, animals bites, and so forth.
The plastic surgeon will access the patient and determine if Dermabrasion will give the best results or if lasering may be more beneficial.
With regard to microdermabrasion, I have heard that a good scrub applied with a wash cloth in a circular motion, may be just as affective as any spa treatment, at a huge fraction of the cost.