You'd be a fool to only focus on OIDC, at least for the next few years. As Azure gobbles up the Enterprise segment, Azure AD can be used to provide OIDC which will be nice. Though most admins who we work with are far more comfortable with SAML.
To be completely honest, the major of customers who are primarily interested in OIDC are coming from Google and/or GCP shops (which are few and far between).
There's a subtle difference where the de facto best practices deployment for SAML includes cryptographic audience restriction: each IdP/RP pair generates a key just for that interaction. With OIDC, GSuite (or whatever) authenticates you to the RP. With SAML, _a SAML configuration on your GSuite install does_. You want this, because optional (largely: non-cryptographic) audience restrictions fail more than half the time and when they do they fail open.
(If you're thinking "if that's true why isn't all of this just Kerberos": you're not wrong, at least from a protocol design perspective.)
As a result you can have identity provider sitting in an unreachable / private network.
Or.. Your identity provider doesn't even have to be a network service at all. We have some integration tests around systems using SAML for authentication. SAML authentication statements in test environments are generated by the test suite and fed to SPs via Selenium controlled browser.
And If they don’t like JWT, why don’t they use something else?
They can't walk JWT back now without breaking existing apps, because parsing it yourself was advertised as an option.
However OIDC is catching up quickly. It's supported by ADFS 2016, Azure, Google and all major IAM products now. It's also a lot easier to integrate, to use and to debug.
So both will be supported by all companies over the coming decade. Even dinosaur companies like banks that are very backward, because they follow Microsoft lifecycle.
I’m not looking for 1 answer perse, mostly looking for opinions.
If you want one target: you’ll want SAML to federate against ADFS. That gets you going with an open standard and targeting one of the most common IdPs.
[0] https://www.internet2.edu/products-services/trust-identity/g...