Tailscale and Teleport are similar, but operate at different levels of the network stack. Tailscale governs access and routing at L3 in the OSI model. See Hashicorp's Boundary or VPNs for alternatives. As a generalization, Teleport works at L7 -- doing auth and routing at the application protocol (ssh, psql, k8s) level.

There are ups and downs to both: L3 is relatively technology agnostic (e.g. you don't need different support for connecting to a database vs ssh). L7 auth & routing gives greater protocol introspection, but means more work to support different use cases.

Depending on your scale and use case, the right answer may be both: Do 2FA for both network access (are you allowed to send packets to the ip:port) and application access (are the packets you send allowed to sign in to the database as an intern or a admin?). The most important part is to get a hardware token and SSO on the path to access.

Disclosure: I work for Teleport. I also think Tailscale is awesome and run it for my home lab.