In truth to be healthy you really can't just pick one and think you've got it covered despite having some overlap. Having said that there's a long standing axiom which (with various phrasing) states "You can't exercise your way out of a bad diet.". For the vast majority of people the caloric deficit brought about by even a pretty good workout regimen falls short of what anyone would describe as a "bad" diet. The biggest problem is how freakishly easy it is to overdo things. To put a face on it a Big Mac combo with only medium fries and regular soda is over 1100 calories.I would argue regular vigorous exercise is more important than diet.
Obviously if you get way up the ladder to people that are genuine "athletes" and can require high caloric loads just to maintain then the margin for error will be greater.