The airframe on the 737 is designed to be a high-cycle, low-maintenance airframe, while the A320 comes from the factory with a lower design goal. The Airbus supplementary goals, while still falling short the out-of-the-tin 737 DSO, can be extended (ESG I, ESG II), but these programmes come with extra cost and more time out of service for the added maintenance required to achieve the extended life goals.
Even with the Airbus ESG extension, the 737 still remains a longer lived aircraft - and thus worth more money in the secondary market. In addition, maintenance costs on the 737 are much lower than its European cousin, and those costs will only increase over the life of either aircraft.
All the above said and generally known, the higher maintenance costs and lower life limits have not hindered the popularity of the Airbus narrow body, with a great majority of the world's airlines saying 'yes' to Mr. Leahy over the past decades.