Be careful with these sorts of generalizations when it's to related, but not identical, species. We can see with Bonobos and Chimpanzees that even within a genus there can be big behavioral differences.

For instance, your Hare link goes to Lepus.

Non-domesticated European rabbits (Oryctolagus) exist. If you don't trust that there hasn't been cross-breeding with domesticated rabbits, then Caprolagus would be a better comparison. Even Sylvilagus, phylogenetically closer to Oryctolagus than Lepus, is behaviorally distinct (not existing in warrens).