Interesting, I didn't realise they were powered and all different..
They are all powered, generally speaking. The GPS signal levels are so low you really need gain at the antenna to make the system work. Hence most GPS receivers supply phantom DC power up the antenna cable to power an LNA on the antenna patch itself.
On all devices I've come across this has been +5v, although I would imagine most "universal" GPS antennas probably work over a reasonable range of voltages. I guess it might be lower for handheld devices which have lower supply voltages.
I can't see a problem with measuring it with a mutimeter, as long as you're careful not to short the inner conductor to the outer.
I must say my TomTom has been great. Bog standard base model that I bought years ago. It's been bounced around in the Westfield in the rain, has lunged off the windscreen numerous times yet the hardware is perfectly fine. If I do have a gripe with it it's with certain features in the software but that's true with every system I've used.
It's certainly a lot less tedious to enter a destination than an NCDC system and the only time I have problems with satellite reception is in tunnels, so I haven't found the need to worry about an external antenna.
Kevin