320s because of their higher landing gear require more equiptment to turn them around (belt loaders, stands for fuelers etc) that make them somewhat slower to turn around than a 737.
The 320 is actually not a good matchup with the 737s. What the 320 ideally replaces is the 727, and since there were 1830 of those built, Airbus had a huge instant market which boeing abandoned. (The 757 was the replacement for the 727 but it was larger and therefore not a direct replacement)
I have flown both and the 737 is THE quick turn machine, which is what short haul flying is all about.
Cheers
Wino