[skissane]

I’ve personally experienced insurers having different “levels” of plans, and some employers pay for a higher level of cover than others. Once, I switched employers, my new employer perchance used the same health insurer as my old employer-but at a lower level of coverage.

[dkh]

I've seen and experienced this as well, but not to the point where calling the same doctor for an appointment would get me in earlier or later. More typically I have access to different doctors altogether, or need approval for certain doctors, or have different out-of-pocket costs.