There are advantages and drawbacks with each solution, of course ; here are a couple of thoughts :
- Web applications are easy to update : you have control over the server, and you deploy whenever you want
- Web applications pretty much garantee that all users are using the same version of your application : the current one (i.e. no-one is running an old, non-updated version)
- Desktop application can use more memrory and CPU : the limit is on the user's computer (and there is one computer per user), and not on the server (shared by several users)
- Desktop applications only work on systems you developped them for (i.e. windows/Linux/Mac 32/64 bits)
In your case, if most of the work is done by the external database, I suppose the web/desktop application would only be a front-end that sends queries and display data in return ?
If so, you probably don't need much power on the application-side : almost everything will be on the database side, which is necessarily shared amongst users.
In such a case, I would probably go for a web-application : easier to update, works on all platforms, doesn't require much server-power.
(Disclaimer : I am a web-developper -- so might be a bit biased ^^ )