Selfhosted

The nice thing about an SSH tunnel is that it only exists when you create it, on the fly, per use, with your SSH credentials. And it is only accessible if you possess an authorized private key. An SSL connection through a browser doesn't fill the same role. SSL provides privacy and security in the communication between server and client. It doesnt have authentication built in. If you are accessing through a web browser you are probably talking to a web server, but SSH allows you to tunnel any protocol (web, rdp, whatever) forwarding traffic, encrypted, across a chosen port.

Edit to add a bit more: attack surface. SSH is a very robust and heavily used protocol with well tested implementations. Other solutions involving the web are probably involving software stacks with layers of configuration, more rapid iteration to add features and therefore a higher probability of vulnerabilities existing or being introduced in updates. Is this consideration relevant to your use? Probably not, =P but you asked about what might differentiate these two approaches from a security standpoint.