What would be the difference if I use the Web server instead of dedicated server for protein modeling and docking?
There should be no difference in output.*** The big difference is likely going to be in the size of the analysis you can perform, and how fast the analysis is performed. A lot of web-servers have a job size limit to prevent one person from hogging resources unless you buy greater access. On a public web-server, your job is queued with everyone else's. If the server is in high demand, you may have to wait along time for your analysis to kick off.

***: I said there should be no difference in output and that is true if you set up your server the same as the public webserver with the same parameters used for analysis execution. This could be a good or bad thing depending on what you are trying to accomplish. Some public webservices do not give you access to all parameters, so setting up your own may give you the ability to tune your analysis to a greater degree.