If I install the 50A GFCI breaker at the house panel, doesn't this offer better overall protection over the entire run of cable than if I install it at the box outside? So why wouldn't I want to install the GFCI at the house and the non-GFCI at the disconnect?

I'm not an expert, but from the research I've done, the down-side to installing the GFCI at the service panel is that if there is a long run of cable from service panel to disconnect, the GFCI breaker in the service panel is prone to nuisance tripping (the GFCI works by comparing the current going out to the current coming back so if the difference is more than a few milliamps, it will trip).

Otherwise, yes, having it at the service panel better protects humans over the entire length of cable.

Regards,
GH