Batman: Gotham Knight, Wolverine Recommendations
For a starter, both Wolverine & Batman are based on famous comic book characters, created respectively by Marvel and DC comics. The characters are also quite similar: both vigilante anti-heroes, who are struggle to cope with their dark past, while still keeping their human nature and will to do good.
The stories also follow a similar path: both protagonists are usually seen fighting against groups of enemies while trying to save or protect someone.
Overall, I found these two anime to be quite similar, not only in the characters are storytelling, but also in the mood they create and their visuals.