I've been seeing a lot of these on the local sites like Groupon.  They really can be quite different depending on what product line the spa uses, the experience of the aesthetician, and your underlying skin issues, if any.   If the spa uses a type of peel (usually these are glycolic) that doesn't self-neutralize, there is a risk of getting burned.  There is always a small risk of having any allergic reaction to a product.   That risk is the same at a dermatologist's office, but if it happens, you have a doctor right there to take care of you. 

My main problem with spas is that they often do procedures like peels with no knowledge of what to do if something goes wrong!  Then, their poor clients end up in our office. See my guide on light peels for more information.  Dr. I