Web applications solve SOME (not all) problems better and more easily than desktop applications.
In favour of Web Apps:
Deployment: As far as the client is concerned, web apps are zero click deployment. Nothing to download, nothing to install, just go to the web site.
We supplied a desktop app for calculating income compensation to our clients for free. Accurate calculation is required by law, so they had reason to use it, but only 30% did. Now it is a web application and 95% use it.
Updating: Web apps are always up to date. With desktop apps it is always a struggle to get users to upgrade to the latest, fixed, version.
Friction: I sell shareware apps on the side. In order to get someone to buy my software, I need them to download it, install it, try it, go to the web site and then pay for it. As a web app, they can find it, run it, and pay for it without leaving the browser. Whether this will give me more sales is open to questions, but I would like to know.
Connectivity
Web apps are, by definition, online. It is trivial to share data between multiple users in different locations. Doing this for a desktop app is harder.
Cross platform Web apps run on nearly anything from a phone on up.
Subscriptions:) It is easier to sell a web app on a subscription. Users aren't so keen on this for desktop apps.
In favour of desktop apps:
Performance: In my experience, desktop apps perform better than web apps. E.g. my income compensation calculator is faster on the desktop than on the web. This can be mitigated by ajax and clever programming. In some cases, eg heavy server side calculations that can be farmed out to a server somewhere, a web app can be faster e.g. Searching your emails in gmail.
Functionality: Desktop apps still have the edge here. Web apps are gaining here, but still behind for now.
Offlineability: Still important for some. It is possible to get web apps working offline with gears etc but it adds a degree on complication to building it.
It depends on what you want to do, and who you want to sell it to. Photoshop won't be web based for a while yet, but Stack Overflow would be pointless as a desktop app..
Finally Balsamiq mockups is available as a RIA, and as a desktop version. In interviews, the own states that the bulk of sales are coming from the desktop version.