We had a similar situation and went with the approach of having a separate installation for the help desk and the developers. However, mainly because the help desk is not just a customer support group, but also does our internal network and general IT support. Also, we made this decision while we were still using FB4, so the dynamics may have changed. If it wasn't such a hassle to merge systems, I think I'd seriously consider merging them back.
Ticket History:
If there is a lot of potential for tickets to move between support and the developers, you are probably better off with a single system. If necessary you could do some clutter hiding for the support folks by giving them a separate project code (even if it is the same app) for their tickets and removing their access to the developer project codes. Also, if they can be trained on the use of filters and search axis it should mitigate some of those concerns.
Upgrades/Downtime:
Since we can upgrade the sites independently, we can patch the developer instance more frequently with updates. If we had to take down our help-desk system there would be a lot more red-tape and we would probably only do major upgrades.
Ticket Numbers:
If you go with the multiple database approach, be sure to configure the case number prefix differently for each installation. Otherwise you will run into trouble/confusion when someone references a case number from one system when documenting a case in the other.
Licensing:
As it was explained to us by FC, not sure if it has changed, but I'm sure they will jump in if my information is out of date. You just need to pay for a license for every individual user of the system regardless of how many installations you have of FB or how many they have access to. So if you have 10 people accessing some combination of 3 FogBugz installations, as long as you have 10 user licenses you are good.
One con to the multi-database approach is that managing your licenses can get a little complicated because the built in licensing mechanism really wasn't designed to manage users/licenses across installations, so you will have do stay on top of this somewhat manually.