.honestly Strange New Worlds has given us a decent way to handwave the Constellation's low registry #. have it not be a constitution (or at least, not having started as one) and instead be a Sombra class, which shares a hull but apparently has different internal systems. the ship seen in SNW was the USS Peregrine, with a registry of NCC-1549, suggesting it is probably older than the Enterprise, which itself was established as having been around for a couple decades by the mid 2260's of SNW
i tend to think that the Constitutions were derived from the Sombra's much the same way that the Ticonderoga class guided missile cruiser was derived from the Spruance class Destroyers IRL, where they took the hull design and engine systems of the Spruance, and added heavier armaments and defenses to it.
in the Sombra/Constitution's case, i figure the Sombra class probably carried a lot lighter armament and weaker shields, and was probably not meant to be a frontline combatant the way the constitutions ended up. their one stated performance detail is that they were faster than the constituitions, which i'd assume would mean they could sustain high warp longer (since the the connies already can hit some pretty high warp #'s for the time.. but if you can keep those upper end #'s going longer you'd get places faster), probably a side effect of having a potent warp core but not a lot of stuff other than the engines to use its power on. which might have been why the Sombra class got used to build the connies.. if a ship has power to spare, accepting a bit of reduced performance to get heavy guns and strong defenses without having to design an all new hull and powertrain would be convenient. though in the process the crew apparently more than tripled.
i tend to think that the Constitutions were derived from the Sombra's much the same way that the Ticonderoga class guided missile cruiser was derived from the Spruance class Destroyers IRL, where they took the hull design and engine systems of the Spruance, and added heavier armaments and defenses to it.
in the Sombra/Constitution's case, i figure the Sombra class probably carried a lot lighter armament and weaker shields, and was probably not meant to be a frontline combatant the way the constitutions ended up. their one stated performance detail is that they were faster than the constituitions, which i'd assume would mean they could sustain high warp longer (since the the connies already can hit some pretty high warp #'s for the time.. but if you can keep those upper end #'s going longer you'd get places faster), probably a side effect of having a potent warp core but not a lot of stuff other than the engines to use its power on. which might have been why the Sombra class got used to build the connies.. if a ship has power to spare, accepting a bit of reduced performance to get heavy guns and strong defenses without having to design an all new hull and powertrain would be convenient. though in the process the crew apparently more than tripled.