Hey, here's one I can help answer (for a change)
KC-10 crew chief here... with an awful lot of time having to fix damned booms and drogues.
First, keep in mind mission drives the gear.
Some of you have touched on a little of the why... but wait! There's more!
For the AF that has a lot of heavies to refuel (as well as puddle jumpers) it needs to move a lot of fuel fast and the boom does that. Also, must consider that the boom is far more stabile in flight. (while I don't recall the fuel flow rates exactly, I recall that a KC-10 can transfer as much fuel in 5 minutes as a gas station pump (for autos) can in 24 hours... or something like that, don't quote me exactly)
The Navy for the most part doesn't have to move a lot of fuel at a time as most of the acft are small and also there's the whole landing on a carrier thingie which helps to keep the acft size to a minimum.
The real reason is HELICOPTERS! It's awfully hard to fly a boom down between spinning rotor blades. Look at sea stallions or even Jolly Green Giants with the big probes that jut out in front to avoid the blades. The drogue just has to come in on the horizontal (rather than a diagonal for the boom). So, for standardization, Navy has probes on all it's acft.
Also, the 135's and KC-10's fly too fast for heli's... so even though they have drogues for navy, they don't do heli's.
Trivia: On KC-10's, if A-10's are in the mission profile, they must use KC-10's that are not modded with the drogue pods on the wings. This is because of drag and lift restrictions... the KC -10 cannot fly slow enough for the A-10 to keep up when the tanker has the drogue pods installed.
And remember: no one kicks ass without tanker gas! LOL