The rating for the compressor is the largest draw it will have when operating. The start up draw will be much more. A lot depends on the compressor as all are not the same. I have a Hitachi job site compressor that sometimes flips a 15 amp breaker. I never run it with an extension cord since air hose additions make up for extended runs.
Sometimes, if powered by a temperamental circuit, I'll empty the tanks so the compressor is not initially starting against full pressure. If I warm it up like that, it will operate on a 15 amp circuit.