The timeline is the same up until Remake, so it makes sense that Crisis Core wouldn't be different except for one key point about the main character.The original Crisis Core was a direct prequel to the original FF7. The story leads right up to the events of FF7.
But since the remakes are going a different direction with respect to the original story, we can only assume that is still the case with Crisis Core remake. If it's anything like FF7 Remake part 1, there will be a major divergence and certain characters fates will play out differently.
Not going to spoil either, it's worth playing both the originals, imo.
Advent Children glossed over most things, but if you're looking for cliff notes, sure, go watch it. Technically, Advent Children is a sequel to FF7, so normally it's something you'd watch after both the original games.