There are a few things that make me value the desktop over the web, as a user. First, no surprising interface changes. If I install a new version and dislike it, I can go back to the previous one. Second, if it doesn't need a network connection by its very nature, it'll work fine without one, removing a point of failure. Third, local data storage with optional cloud synch is the best of both worlds. Fourth, a polished native program will have more predictable timing than a similarly-polished web app.
Both have their place. I'll go to a web app for asynchronous communication (e-mail, forums, social media), for one-time reference or reference to things that change often (wikis, imdb), and things that I intend to use for a short amount of time, or which wouldn't be worthwhile to download and install on a couple machines.
Putting things on the web has always felt to me like a compromise of usability and predictability in favor of convenience of access[0]. I like storing my data locally until such time as I explicitly decide to store it online. I like knowing that I can continue using the software, regardless of the fate of the developer.
[0] Given internet connectivity and continued operation of the company providing the software