A lot of XI's story was coherent -- XIV's is not because it was originally designed to allow any disciple to do it, basically which is what destroyed any possibility of doing it in a group or difficulty. This is why there's an obvious difference in the direction of the game (and more towards how XI used to be) once Yoshida took over because now you can do story quests in even a small group and hell you even get group cutscenes which would have made quite a few of XI's cutscenes that much more epic, for example:

Promathia form 2 cutscene, Odin versus Alexander, Battle of Jeuno etc.

Later XIV cutscenes and story quality has gotten better, but the main reason CoP is held in high esteem is because whether someone wants to admit it or not, it had a mix of everything you could want -- difficulty, doable at the lowest possible level (30 - 40 for most of them), great storyline, requires teamwork (which isn't a bad thing, despite popular belief) and a great reward after all of your hardwork pays off, and the reward was threefold -- access to a beautiful location (Al`Taieu), access to end game content (Sea Gods, Limbus, Omega and Ultima rematch for gear) and a Ring based on profession path (Melee, Mage or Tank.)

This is why CoP was great and what they really should have done for XIV originally while having access to greater set of technology to do even more, not less.