There are two kinds of feedback: operational feedback and satisfaction/loyalty feedback. For operational feedback use mystery shopping. For satisfaction or loyalty feedback use customer surveys.
The question is not which one to use because they are two sides of the same coin. Both are needed. Customer surveys provide information about how customers feel about their experience, but provide little information about the process behind that experience. Mystery shopping on the other hand measures the processes that create the customer experience. The most important of these is the sales process.