There are very obvious pros and cons to creating web applications on the Internet. While desktop applications continually struggle with cross-platform compatibility issues, often fraught with completely different rules for handling code, Internet applications are much simpler to port between browsers. Combine that with the fact that only a few large-scale browsers contain the vast majority of the user base, and you have a means of deployment that is much more stable across different users.
Web applications, on the other hand, can be located at one single server location and accessed by all. Any changes/improvements to the functionality can be delivered in one central location and take effect immediately. Far more control is left in the hands of the developers, and they can quite often continue to create and maintain a superior product.
There is also the much-appreciated benefit to being able to create and maintain a single code base for an online application. If you were to create a desktop application or learn some web application and then deploy a patch for a bug fix, the user must either reinstall the entire software package or somehow gain access to the patch and install it. Furthermore, there can be difficulty in determining which installations are affected.
Naturally, everything comes with a price. While delivering an application from a central server location is quite nice from a maintenance point of view, the problem arises that the client needs a means to access said point of entry. The Internet provides a wonderful way to do this, but the question of speed comes into play immediately.