We don't really know whether the prestige of a Constitution
class starship lives up to our speculations and expectations.
Back in Pike's days, the ship seemed to have fewer people aboard and limped back home after suffering, what, seven casualties? The CO also wore much less braid, and didn't think much of himself. With Kirk in command, the ship mainly ran errands, a type of behavior not associated with capital ships in the real world. Perhaps Constitution
class ships are famed for being so darn expendable, being always sent to places of high risk, and being commanded by daredevils and mavericks who are a class apart from the more sedate Commodores who command the capital ships. Although if one survives commanding a heavy cruiser, one may advance to command a capital ship eventually...