I needed to add a few custom fields for JIT provisioning that weren't present in the default configuration. After making my modifications (and writing a test class for Salesforce generated code), some of my existing SSO configuration settings are no longer working.

Example
UserRoleId and ProfileId could be set by its name instead of actual Id. Using the generated class, you have to use the actual ID. This is fine by me, but the unpredictable differences annoy me.

What other differences are there between Standard and the generated "Custom SAML JIT with Apex handler"?

Shouldn't both be the same, allowing you to rely on the Standard where possible? And if necessary, make modifications through the generated class, but still assuming all else will work the same?