I'm thinking about getting
this antenna for use with my GRE PSR-500 in my car to scan 800Mhz frequencies. How much will it help? Will I see a big difference in reception reach or reception quality? What makes the actual transceivers installed in police and fire vehicles get such good reception? Is it the antenna? Thanks.
That antenna should do fine for 800 (and the nearby 700 & 900 MHz) bands on a scanner. That said, you may experience some systems that may perform poorly due to a too strong signal (although it'll mimic a too weak one). This is generally on a simulcast system where several towers broadcast on the same frequency (or frequencies) and with a strong signal the scanner tries to process the combined signals from multiple towers, which causes distortion and generally bad performance. With a weaker signal, only the closest tower comes through and there's no mixing and the associated distortion.
Why do actual transceivers work so well when scanners don't (a slight modification of your question, but one I think gets to the meat of your question)? Basically there are two reasons, bandwidth of the radio and cost.
A scanner is designed for a very wide frequency range to receive signals on, so the circuits must be designed to allow this wide path through (like the water flowing down a garden hose where the flow may move out a bit away from the end, but quickly drops to the ground). These circuits must be optimized to allow fair results over this wide frequency range (with nothing really great, but nothing really poor either). A transceiver is designed to work on a very narrow band of frequencies (as compared to a scanner at least). The circuits can be designed very optimally for best performance over that narrow frequency band. Since they don't need to worry if they work at all outside of that range, they can be made to work really well within it (like that same garden hose after you stick your thumb over the end to create back pressure, causing a long powerful stream when the water leaves the hose).
The relatively low cost of a scanner forces the design and components to be lower than a high priced transceiver would allow. This allows specialized designs and higher quality components to be used. While adding a specialized circuit to correct issues (like the simulcast distortion problem) is easily funded in the multi-thousand dollar radio, it may not be possible (financially) on a scanner selling for a small fraction of that.