I've never ran a hidden service but I think the advantage of running a web server via tor (as a hidden service/.onion) is that people can visit your site yet not know where the server is located.  This makes it possible to run controversial sites with much lower risk of getting shut down by the authorities. 

Hidden services are more secure than clearnet services in the sense that the client and server don't know nearly as much about each other as they do in the clearnet.  Browsing a clearnet site via tor offers the client the protection of tor, but information about the server (such as IP address, Internet service provider, physical location, maybe name of the administrator/owner via WHOIS records) is still in the public.

You may as well stick to the clearnet if you're running a non-controversial/completely legal (whatever that means) site and then encourage visitors concerned about their privacy to browse via tor.

You'll probably want to stick with a tor hidden service (".onion" site) if you're running a site that might normally get shut down by your local authorities.  This is presumably how Silk Road remains in business.

I think all traffic through tor is encrypted which removes the need to use encryption on the web server level when running a hidden service, but clearnet sites can offer encryption through HTTPS.

The advantage of clearnet sites is accessibility by non-tor users and much greater speed than you'll ever see on tor.  The advantage of tor hidden services is protection of the server/site owner.

Good luck!