I just pulled out my bags to compare... haha. The crave is JET black. No hint of gray what so ever. But the caviar used is definitely different from the classic flaps. The crave caviar is softer/sort of distressed but still feels durable. It's also shinier, almost like a gloss. The leather is not stiff like the classics, so it can crease/collapse a little bit at the top if you put heavy things in the bag.
I definitely don't think the bag is too big. I think it's roughly the same size as the classic jumbo? The strap isn't super long so it doesn't look awkward single strap.
Hope that helps!