Scored both ways, the alternative first. These pages are read by the vendors they name, and a comparison that loses no rows is read as marketing.
Complete control, no vendor, and for a single-organization deployment it is a few hundred lines around an existing JWT library. Many teams should do this and the spec on this site is public so that they can.
The value is in two parties agreeing on the same format. A private format verifies only inside your own walls, which is the one property the whole exercise was for.