My vote would be doing a little research to see what band or bands you need to monitor and get an antenna that's designed to cover those specific bands. If everything in your area is on one or more of the systems in the 700/800 MHz band, get an antenna optimized to cover that band. If you live in an area with mostly folks using the 150 and 450 MHz frequencies, get a dual band (2/70) ham antenna. Doing so will get you an antenna designed to do a good job covering what you listen to (and it should work OK on strong signals on other bands, but don't count on that, it's just gravy).
If you're one of those rare folks that actually need coverage in the VHF-Low (30-50 MHz), VHF-Hi (140-160 MHz), UHF (430-500 MHz), AND 700/800/900 MHz then you're probably stuck with a wide-band (but low performance) discone or ST-2 type antenna.
An antenna is designed for coverage over a set frequency range (or perhaps multiple ranges). Trying to extend coverage beyond that is somewhat like trying to use a light-duty truck to haul a heavy duty load. It may work a bit for a while, but if you over do it too much, you'll end up with bad results (like a blown engine and/or transmission in the truck or noisy signals on the radio).