Not a quantitative test, but real world:
My office is in a basement, 1/4 mile from my 800MHz trunked site. I have a Uniden 895 scanner sitting on a table in my office with the stock telescopic whip. Next to that is an Astro Spectra consollete with a 3db gain antenna mag mounted to the t-bar ceiling over head. Also there is an MTS2000 with the stock whip antenna.
Obviously the A/S and the MTS2k work better than the scanner, but I'm close enough that it doesn't make that much difference.
Reason:
Specific 800MHz antenna will outperform a telescopic whip. I could likely improve the scanner reception by using a dedicated 800MHz antenna, but I need to listen in on the two VHF systems also.
The front end of the scanner is REALLY wide, so it's not specifically tuned for the band. Also, the wide open front end picks up a lot of noise from all the other crap down in the office.
A radio specifically designed to operate on one band will outperform a wide band receiver in most cases.
Also, an antenna specifically tuned to resonate on a specific frequency will outperform a wide band antenna, again, in most cases.