Both suit people who want a life rather than a package, which is why this comparison is usually between two long stays rather than two holidays.
The northern advantage is quality of life per baht: cooler months, lower rents, a walkable centre and an easier pace. Training there is good without being brutal, which suits most people better than they admit.
The Bangkok advantage is the ceiling. If you want to know how you compare to people who actually fight, that answer is available here and is not really available in Chiang Mai.
The thing people miss
Both cities have an air problem, in different seasons and for different reasons. If you have asthma or you are training twice a day, check the season before you book either.