No I don't have a power meter. I know the Black works on a USB 2.0 port of my laptop and my desktop too, so it uses less than 500mA. From my experience working with Ti's stuff, they are often pretty good about power consumption though.
My main problem with the Pi is that it is very finicky... plug a USB device in, and it dies/connection drops and all kinds of weird things happen. I have seen none so far on the Black.
Isn't the finickiness related to power consumption? USB is only rated up to 500mA, so drawing too much power from the Raspberry Pi's own USB port will cause all sorts of havoc especially when the RPi itself is powered off another computer's USB port.
In fact technically RPi model B's official spec is that it requires 700mA. You can often get away with less, but you'll definitely start to hit 500mA+ under stress and with peripherals, which is above what USB can officially supply.
Your best bet is to get a nice solid cellphone wall-wart type charger, preferably rated 2A and up. With enough juice powering the Pi, all the issues relating to USB disconnects, freezing, and ethernet dropping stop happening.
Gonna guess that the stability you're seeing with the beaglebone is just from its much lower power requirement.
I can vouch for this. I use a Blackberry wall-wart type charger for my Pi, and it's been rock solid. I only power it down it when I'm off travelling someplace for more than a day.
if you haven't found an answer to this by monday, send me an email (notatoad-gmail) and i'll let you know. doing a power consumption test between beaglebone and beaglebone black is on my to-do list.