Hi Enine,
I've done quite a lot of research in that area recently, and it seems to me that there are a few differences that seem to matter to many:
Trunking
If you're in an area that has trunked systems, you'll want to get a trunk tracker. Otherwise you won't be able to listen to the trunked systems. To find out if your area has trunked systems, check the RR database or Google your city for frequencies and systems.
If you will be listening to Motorola trunked systems, make sure that your scanner will support rebanding or you'll have an expensive paper weight on your hands. Check the rebanding thread in the RR forums for more info.
APCO 25
While I don't yet know all the technical details, if any systems that you want to listen to are using APCO 25, you'll need a digital scanner that can listen to digital channels. Be prepared to spend a lot more money! I opted to forgo a digital scanner right now since systems in my area are still analog, but with my luck, they'll announce an upgrade next month and I'll be out of luck.
Military Freqs
Some scanners don't pick up military air frequencies. (The one I purchased, Uniden BC-246T is one of them), and so you cannot listen to military pilots at air shows, etc. If this is important to you, keep that in mind.
Frequency Layout
Radio Shack (and others) scanners store memory in banks. On a 1000-channel scanner, you might have 10 banks of 100 channels each. I actually prefer Uniden's approach which is to store channels in systems of no particular number. The reason that I prefer that is that you can only store one type of system in a single bank of a RS scanner. If you only have 4 frequencies that are Motorola Type II trunking systems, the other 96 channels are wasted. In the Uniden system, scanner memory can be fully utilized.
With all of that said, I will tell you that I've been out of the scanning world for about 20 years and all of this is new to me as well. I've been heavily researching for the past couple of weeks to get up to speed (this site has been a tremendous resource), so I'm sure I've left off a lot that others will add.
Have fun!
Jim