I could make an argument for baseball or basketball. In baseball, I think it requires a whole lot more in terms of talent development and off-season preparation. Working with hitters, fielders, and pitchers on technique to help them develop is much more important than the off-season preparation for basketball. Basketball doesn't require as much technique development, and it doesn't require nearly as much tweaking in the off-season.
As far as in-game coaching though, I think basketball requires more. As a manager, once you get to the game, you can call steals, bunts, etc., and you can change pitchers or pinch hit, but other than that, you're basically just relying on your players to execute. In basketball, you have to be a lot more active, rotating players in and out, calling plays, deciding when to press and when not to press, when to switch defenses, etc.
And yes I believe football is the clear No. 1 in terms how much the in-game coaching and also player development are important. You can't just run a bunch of athletes out there and win at football. To an extent you have a better shot at doing that with baseball and basketball.