I've used ssh for terminal use and for tunneling for years and years.
Now, I exclusively use openVPN - ssh is only used as a backup, in extremely rare cases.
The biggest advantage of openVPN is convenience. With ssh, I used to have issues with accessing intranet services like mediawiki or redmine, due to my bifurcation of DNS services for the intranet (private DNS) and extranet (public DNS).
Now, with openVPN, everything just works.
My external ssh forwarding is also no longer necessary, as all machines look like they're on the local subnet. So another advantage is further limiting access to your intranet to one point, especially if you previously opened many ports via port-forwarding to your local machines.
Previously, I was hesitant to use VPN as setting up an openVPN server on the intranet (and routing through to it) seemed like a hassle, and perhaps requiring non-trivial setup. Also, I think in the olden days, performance was a concern, but with hardware so fast these days, that also has become a non-issue.
With an openVPN server on the router, it's in the perfect spot in the network, and the setup was easy.
I highly recommend going from ssh to openVPN.
Addendum: My recommendation is based on my experience and requirements. I do not know if you use anything else besides terminal services (and if it's just for one machine on your intranet). You should evaluate your situation and see what works best for you.