[korethr]

What is the cause of the excess heat transfer? Is it mainly an excess pulse duration? I notice that the project in the OP was being pulsed on the order of 100s of ms, long enough to get a visible glow. Or is the excess heat caused by the fact that the OP runs at constant current for the entire duration of the pulse, where a capacitive discharge design is going to have the current falling off during the pulse? Or is it a blend of both?

[CapstanRoller]

It's excess pulse duration coupled with insufficient current. Capacitors can dump all their energy almost instantly (on the order of 1000s of amperes), but transformers are much more current-limited due to their design. It's analogous to using a press vs a hammer.