Both have a ML with a hidden identity for the reason of finding their father's killer. Both MLL wear a simple mask and costume to disguise themselves while also making their alternate selves famous.

Both seem to have FL crossing into a drama world where she's fated to die and manages to prevent such fate.

Both have similar vibes. MLs use extreme means to achieve his goals. In Awaken, the ML is clearly more emotional and has a clear bottom line. In TMWYS, it's a lot blurrier. FL clearly likes ML in Awaken but that doesn't seem to be the case in TMWYS.

ML accidentally time travels and meets his parents' younger selves...
He brings modern technology with him too
Similar story where ML learns of the hardships of his parents

Similarly has reincarnations of deities and mortals. One immortal remained alive for thousands of years .

Not sure why they decided to change actresses in Ice Fantasy Destiny tho. With the original actress only making a cameo appearance towards the end.

Similar premise: Alien beings treated as gods. Romance between one of those said gods and a female warrior. Battle of the gods affecting the human realm.

Another adaptation of the same novel.

Both have a male lead who time travels to the past into a Harem. Similar comedies in both but Man Comes to Tang Dynasty focuses more on the comedy aspect while Concubinage Record focuses more on case solving.

Also, the time travel is completely logic-less in Concubinage Record. ML possesses a body to time travel yet modern equipment also time traveled with him somehow.

Both main character(s) time travel to the past more or less due to a song. Similar school youth vibes and are about trying to prevent someone's death.

Both have people going under cover, good guy vs bad guy tho the good guys operate in a gray area...

Both are interesting

Both portray a killer under the guise of a regular person. Kill It is definitely darker but both leads are trying to use their own methods to do the right thing

Okay I know this is a stretch here but the dynamic between the female and male leads are similar... FLs are super smart while the male leads are full of passion, but not exactly the brightest... It's also the FLs that paves the way for the MLs' successes...