Both have the same actress with similar basic plot.
***spoilers***


In Scarlet Heart first she's a commoner, becomes a maid in the palace and climbs to higher position. First she loved a married man they couldn't be together and she ends up with his brother who comes the king.
In Imperial Doctress she climbs from commoner to doctor in the palace. Can't be with her first love because he got married, while he's brother the emperor is in love with her.
(of course first guy has an evil wife who wants her dead in both of them)
I think they are both really similar in the main plot and the love triangle.