Using the SS vs. fixed, all other things being equal model that we are given, here are my two main ideas regarding efficiency:

Energy transfer. On a SS, the force from your leg goes chain->freewheel cog->some teensy parts within the freewheel->hub body. On a fix, it goes chain->cog->hub body. The SS has more steps of energy transfer, and thus greater quantity (however minute) of energy lost to entropy.

Flywheel effect, or "crank inertia": Assuming that this phenomenon is viable, it would seem that pedaling a fixed gear is even more efficient.

I haven't heard anything to suggest anything that makes fixed a better workout than free. If anything, all (theoretical) evidence points to the opposite. Also, snowshoeing across the beach while carrying a 50lb pack is a better workout than running. Don't mean it's better.