Let’s look at how 大切、大事、重要 are different.
大事 and 大切
Yep, both have the same meaning. Both mean
This album is important (to me)
This adjective serves to identify concepts as important in a context that transcends one’s own preference and identity.
This album is important (in the history of music)
大事 and 大切 come very close to the English word important. 重要 is about expressing importance in the context of something larger.
I’m basing this off this chiebukuro post.