Both dramas are thriller with a lot of mystery and very strange events.
They tell the story of an unusual cop (male lead character) partnering with a profiler/criminal psychology specialist (female lead character) in the pursuit of a serial killer.
The lead characters have their own personal struggle rooted in their childhood.
They are broadcasted by TvN
However, the male lead character in memorist has super powers but the one in awaken has just great detective skills.

In both drama the main lead can see the past when touching either things or people. There is also a similar style because they are thriller deaming with murder cases. Finally they are all TvN dramas.

In both dramas we have a rich and powerful but dysfunctional and crazy family. We have a chaebol family in Graceful family and a modern royal family in the last empress.
The main vilain in the two dramas are women. They both want to remain in power and are willing to do all it takes for it.
There is also a similar plot with a number of murder cases to be solved and family members of ther murdered trying to seek revenge. The storyline in graceful family is better written and somehow more realistic than the one of The last empress which sometimes lack coherence.
In their own way both dramas are enjoyable and very entertaining.

Both dramas have a similar humor regardless of the fantastic/horror overall theme. In both drama you find yourself trembling in fear one second then the next moment you're laughing out loud.

Both are fantastic dramas portraying Lee seung gi as an immortal being. The romance is both dramas include a mystical male creature and a female human being.
However, a Korean Odyssey is funnier than Gu family book which is more tragic but less scary than the first one.
Both drama are must seen especially for Lee seung gi fans

both lead male character keep acting like kids
in both drama the girl is poor while the man is rich

both drama revolves around undercover operations and jung kuyng ho plays in both.