Main characters time-travelled to Joseon Dynasty from modern day. In MQ, he is a chef. In DJ, he is a doctor. They both used their own respective skills to help out people around them. They both were kinda entrepreneurs in Joseon.

1. MLs are immortals. In Nine-tailed, ML is a gumiho. In YWCFS, ML is an alien.
2. MLs are waiting for his first love (which turned out to be FLs) from Joseon Dynasty.

These two share a lot of similar concept. Both MLs are immortal with supernatural power. ML met first FL when FL was still a child, in Nine-tailed: ML saved FL, in Hwayugi, FL free ML from his prison.

Both are music dramas. Beethoven Virus was my first Korean drama, which display perfect Music Industry, love, friendship and struggles between 3 leads in an orchestra. DYLB also gives me similar vibes.