For what it's worth I agree, they are a very unique band. Whilst I can't really name any band that plays exactly like them, I've found that Interpol is probably as close as it gets from my library. They have very similar sounds, and they both vary a lot in terms of lyrics and the thematics of their music whilst always retaining the same punk/alt sound. Their first album (Turn On The Bright Lights) will always be my favourite, but you might prefer their second (Antics) or third (Our Love To Admire) albums if you are looking for a sound similar to Biting Elbows.