Bulgasal: Immortal Souls (2021)

Both drama revolves around what happened in the past and resolving those problems in the present time while also all the people involve are reincarnated in the present..

Wang Won’s father is the king of Goryeo while his mother is the Yuan emperor’s daughter. He was born with many gifts as he has good looks, the wisdom of a snake, and a magnetic personality that draws people to him. But behind his gentle, virtuous demeanor, he has ambitions to conquer other lands. He has a faithful friend named Rin, who is a royal cousin and comrade with the same ambitions as he does. Then Wang Won has an encounter with a young woman named, San. San was someone that he recalled having met when he was a child and was lodged in his mind ever since. Wang Won sees how bright and confident San is and befriends her as well. But this friendship plants the seeds of tragedy. San’s beauty mesmerizes both Won and Rin and their seemingly strong bond start to fray over one woman…

The only similarity is that they are reincarnated lovers and both think that the other one destroyed their family.
Both dramas are very very different from each other except the reasons above. While bulgasal is a revenge, suspense, thriller drama with a little bit of Melo and romance, "from now on showtime" is a rom-com, lighthearted drama with some ghost and revenge plot.
But both are very interesting drama. Even when Showtime is still on air i recommend it cuz its not looking like it will disappoint it's viewers, and am loving it do much.

859 AD. The once-great Tang Dynasty is now declining. Numerous rebel groups have formed, the largest of which is the House of Flying Daggers, based in Feng Tian county. They steal from the rich and give to the poor, gaining the support of people. The local deputies have managed to kill their former leader, but the rebel group only becomes stronger, due to a mysterious new one. Jin and Liu, two police captains, are ordered to kill the new leader within ten days.

These two are both fantasy k-dramas. Bulgasal is heavier in plot terms including revenge, reincarnation, mystery thriller. Alchemy of Souls is a balance between romance, action and comedy.

-similar plot about reincarnations and meeting people from your past lives
-romantic plot is more fleshed out in CT
-Bulgasal is a more slow burn mystery of the past than Chicago typewriter, but CT also has a mystery of the past the characters are tying to unveil
-bulgasal is more fleshed out in the fantasy aspect
-CT has similar wholesome character relationships like Bulgasal, but in CT they're more friends based than the found family troupe in BIS
-angsty, aesthetic and bittersweet. The osts in both are amazing, acting and cast and cinematography are great in both.
-Both of them are different in terms of setting and time line, CT is more political and set in 1930s Japanese occupied Korea.

Historical and fantasy themes are similar
Beings other than humana
AATM has a more direct romance
Both have ongoing mysteries of the present and past
BIM has concepts of next lives and reincarnations as a major theme, but it's more of a minor one in AATM
both are fantasy based mysteries, AATM set entirely in the historical Era.

Both series are very much a mixture of folklore, folktale, legends, and myth. This aspect differentiates two series from others tagged with a combo of [Mystery, Thriller, Drama, and Fantasy].