There is no hardware interactions, no security dongles, none of that kind of thing. Other than that, what do you mean by "a bit specialized"?
Well then you aren't sitting with a specialised scenario that requires a desktop scenario then... so clearly web dev is the way to go.
If you want to start interacting with offline devices like I do, then desktop apps are a must.
There are a few things off the top of my head that I could mention. Some of these will likely become irrelevant in due course as web tech catches up.
Things like geospatial map rendering of client specific data are a lot faster on the client. Web based applications generally do a better job serving static tiles, or rendering fewer numbers of shapes. If you ask a server to do it, then it will quickly fall over for large numbers of users. Sometimes a customised rendering engine is just so much better.
In some cases you want to store data locally for long periods of time as well (in a disconnected environment) and a db like google gears doesn't always cut it. Also, tools like gears are plugins, requiring the user to "install" something in any case. If that plugin needs an update, they have to allow the update in any case. This doesn't get around the upgrade issues of desktop apps (which can auto-update - take click-once installed applications as an example... you can force updates on next load)
When it comes to the libraries available in the .Net framework for example, there is soooo much more available, that you couldn't possibly do with javascript and HTML5. There are stop gaps, take Silverlight for example. It's "in the browser"... but it's really just a desktop application that the browser allows to show. That's why you can run it "out of browser" as well. There's also a reason why the .Net framework available in Silverlight is only a fraction of the size of the full framework.
What about movie editing and rendering applications. You can't do that in-browser. Even video transcoding done by the likes of youtube is done on servers. If you wanted to do that using what is available in javascript or HTML5? Not possible at the moment.
Another thing to consider is the size of the application. Take Photoshop... it's huge, and it's almost impossible to leverage all that functionality over the web as we currently know it. You'd constantly be downloading modules in a Silverlight / Flash application to get it to function. Jquery is awesome and all, but just doesn't have that kind of capability.
The list goes on and on. As time goes on, there will be more and more stuff available online, but there's a reason people built the likes of flash and silverlight. It's because normal browser rendering tech just can't catch up with proprietary software due to that little requirement called standards. All the browsers have to implement the same functionality for it to be useful in your application. This limits the speed at which new features can be added.
