If you have relatively unlimited funds you can buy and use an active antenna which will cover from 3 to 300 mhz for something like $9,000 per unit. They're used on Humvees, Bradleys, etc. There's an outfit in Beltsville, Maryland that makes them. These are used for transmitting as well as receiving. For your garden-variety scanner I would guess the govt. uses the same units as the civilians do.
Telewave discone. I actually selected that antenna for my own use at work. I have a good high site and needed an antenna that would meet a couple of requirements:
1. Durable, not be damaged by getting bumped, wind, corrosion (we are on the coast).
2. Last more than a few years. We've had Diamonds, and they last pretty well, just as long as no one bumps them. I didn't want to be replacing this one in a few years.
3. Could double as a back up antenna for some of the repeaters at the same site, VHF, 800, etc. At this site they are running 100 watts, and I don't want a cheap ham grade antenna causing problems on public safety systems.
Sometimes it's easy to get money for a specific project, to do it right the first time. If you have to go back later and fix/repair/change something, it gets pretty difficult sometimes. Spending money at the start so I don't have to go through the hassle of trying to find funds 4 years from now. New installation comes out of the project budget. Repairs down the road come out of my maintenance budget. Always better to have the project pay for the right stuff from the get go.
For mobile, it's mostly the antennas that will ship with the Motorola radios, or Larsen. I've used Antennex and Comtelco on occasion. No real reason for one specific brand over the other.