I'm a bit confused? You want to use it with the scanner, AND a few hand-helds? You want to connect a hand-held to the discone and transmit, I assume?
The discone is fine, and always a good match for a scanner that can listen to many different users - amateur, marine, civil and military air and the public and private mobile radio users who use radio for business and leisure. The transmit ability can be useful because the antenna presents a decent enough match for practically all the common transmitters.
The antenna offers no gain performance on all those bands. Band specific aerials might have some gain in some bands - so perhaps producing double or more the signal in certain bands, but performing performing less well on other bands.
The discone has the same gain as the 1/4 wave antenna fitted to some portable radios - IF, and it is a big IF, the radio has a suitable ground plane to enable the 1/4 to be efficient. A quarter wave antenna on a walkie-talkie sitting on the window sill has very little surface area to allow the 1/4 wave to perform optimally.
So the 1/4 wave antennas can be ok, and on a portable, are probably the best balance of performance and size. Moving to VHF it gets a bit worse because most VHF 1/4 waves on portable radios have to be shortened for practical reasons. A 17 or 18" whip isn't the easiest to stick in a pocket.
The Sigma up high (WITH DECENT CABLE) will out perform a portable by quite a lot. frequency specific products are better than discones on those frequencies, but a discone is much better if you need multiple band performance.