Desktop applications give a far superior user experience than web applications.
Sure every option has its pros and cons, but you need to rate these as well. Which is more important to you, user experience or platform independence? We rate user experience above many things. Yes we are making sacrifices, but that's part of life.
One way to convince your superiors is to prove to them that the user experience is lightyears ahead on a desktop application and try to convince them to create a desktop application before making the web application.
We have both at our company and our customers prefer the desktop app over the web app any day. They're quite willing to accept any disadvantages that comes with using a desktop application.
I'm not listing the advantages of a web app in my answer as others have done. Web apps and desktop apps both have pros and cons. Do both! Let your customer choose. Get back to me on the statistics. ;-)