Which technology to choose for web applications with a rich user interface

I need to choose a stack of web technologies to create a Java web application with functionality similar to MS Visio Online or Sparx Web Enterprise Arhitect. So I have a few questions:

1. Does it make sense to write such applications for the Web at all, or is it better to use desctop technologies like WPF?
2. What limitations in functionality will the Web version of the application have in comparison with it's desktop version?
3. What technologies to choose for frontend and backend?

If you have experience in creating such applications, please share any thoughts on this.