You can do both, and leverage both, to improve the capabilities of both. Leave NATO as the standards-definer and overall command structure. But also, the EU should absolutely take more advantage of the economy of scale for big-ticket items like regional ballistic defense, new fighter projects, even submarines and CVNs.
If they do it conscientiously, and are careful to not let military industrial basically dictate procurement policy, the EU could potentially spend less under that aggregated model than they do with individual, independent militaries.
As an American, it’d honestly be great if literally anyone else who was somewhat ideologically aligned with the west would really, seriously underwrite the security of the western world in a military sense.