Neither Google nor VZW services are "active" (ie they don't use power). the VZW service reads the location of the cell tower, while google uses the recorded location of the Wifi hotspot.
It doesn't make the location more accurate when using GPS, but it does help acquire the location faster.
Ok, I don't quite agree. GPS DOES make your phone detect your location MUCH more accurately. Within 3-5 meters some times. The more satellites you connect to the more accurate it can determine your location. This is the most power hungry location service.
Google Services use a database of wifi signals. When Google sends out their street view cars, they are also mapping wifi signals in the area (they might use 3rd party data as well). So, by looking at what wifi signals are around you, they can estimate your location. This uses less battery than GPS, but it still has to power sensors and phone hardware to work, so yes it uses battery. Anything your phone does, except sit there powered off, uses battery.
Verizon services uses cell towers and location information from the cellular network provider. And yes, still uses power, just not much.
Also, different apps use different services, google maps for example can't get a location if you only have on verizon services, and I'm pretty sure the VZ Navigator would need verizon locations on.
and I think Google's location services might use cell towers too... the difference then would be basically what database each is using to map nearby cell/wifi signals then determine location, and how the apps ask for and receive that data from the service.
For example, I don't think Google maps is programed to asked for a location from Verizon Location Services, which is why it doesn't work.
But in the end, GPS is always more accurate, if you can get signal from enough sats. You need at least 3 to determine a position, after that it gets even more accurate.
Test:
Turn off GPS, go into maps, click the location button, then click on your location. It should say, accurate to x meters. Then turn GPS on and do the same, it will be more accurate (if you can get a gps signal.)