They do seem to suck current.
That is a trade-off:
digital: can use a lighter servo, but draws more current
analog: will need a heavier servo, but draws less current

In my case, I will be connecting to a 3 axis gyro system, so any servo will start drawing more curren from all the corrections issued by the gyros. The gyro system vendor recommended an external BEC for the servos, etc. so as not to fry the ESC.

LATER:
I dug up some numbers from my testing (using a Watts-Up meter, connected a 5V BEC via a Silicon diode to drop the voltage a little, and pushing the end of the servo arm against a scale):

HKM-282A analog servo ("2.0g"): ran at ~0.19A peak about when the servo gave way at ~130g (using a slightly longer arm than the 2 digital servos below)
HK5320 digital servo ("1.7g"): ran at ~0.28A peak about when the servo gave way at ~250g
HK5330 digital servo ("1.9g"): runs at 0.25 to 0.30A peak when arm tip is pushed to 400 to 425g (servo still not giving way)

some recent 3 to 4g Walkera digital servos: ran at 0.10 to 0.15A peak when arm tip is pushed to >400g (servo still not giving way)

I stopped at about 400g of pushing because that is almost 1 pound for a servo that will go into a plane with AUW= 6 ounces or less (sorry for all the mixed units).

Anyways, these small digital servos eat up some current, but not that much (looks like < 1A for 3 servos, while I expect more than that for the motor), and not all that much more than my analog. The larger, heavier digital servos have the advantage of using less current to exert the same amount of force that I was using.