Power projection: Navy
Defence: Air force
Air force has a much greater use than pure defense.
I think the specific time also needs to be considered. From 1900 to 1920s aircraft technology was relatively insufficient and so most nations would pick a fleet of dreadnaughts any day.
By WW2 (excluding carriers - which is somewhat of a large exclusion), planes have become more viable, as seen in the Sinking of Repulse and POW (battleship and battle cruiser sunk from land based aircraft).
After WW2, a larger air force would become more important than naval assets as seen by the disappearance of capital ships save for carriers which carry aircraft.
That being said, this doesn't mitigate the importance of a Navy. There is a reason that US is the world's superpower and whilst nukes and its economy play a role, so too does its power projection via the use of its navy. That being said, aircraft are indispensable in this day and age, and if I had to pick between Air force or Navy, i would pick air force.