In my opinion any OCN drama really fits this category as they have a unique style to their dramas, though if you're not into detectives/police etc then you probably want to avoid them.
Vampire Prosecutor and
Dr Frost are the first two I think of for OCN for recommendations, and both are completely different with the aspect of dealing with crime, but are very gripping. I do also want to say
Incomplete Life, though it depends on your taste in dramas, but you are watching Awl which I've heard is similar so I'm throwing it out there. I'd say
Surplus Princess too, though warning that this was cut by 6 episodes and it's not as long as a normal Korean drama, so it did have a few issues story wise. Others may disagree on this one, but I haven't seen a mermaid feature in many Korean dramas. It's pretty fun loving.
The only Japanese one I can really think of is
49 but personally I think the Japanese have lots of unique dramas anyway, so you can just pick any up and it's going to be pretty unique. (Though maybe it's because I don't watch them often. xp) Lastly and again, another short one, is Chinese one
Jenius. If you like Death Note (and if you haven't watched/read Death Note, I really recommend you do!) this has a similar feeling when it comes to having a thought provoking story, though less intense.
I hope I've helped, even a little. :D