Po Boys are supposed to be on french bread, so it's not that, grinders are toasted and crunchy, Hero's are a NY thing and generally are fillings other than italian meats. I never quite understood what is different between a Sub and a Hoagie, both are on Italian bread, but I think a sub can be hot or cold but a hoagie is Italian bread, meat, and cheese and hoagies are never a hot sandwich.
I'd call it a hoagie, but I dont think anyone calling it a sub would technically be wrong.