Both series are made by the same people featuring many of the same actors and sharing several tropes. While the themes are different - City Hunter being about corrupt politicians and crime, Dr. Stranger mainly being about North Korean defectors and corrupt hospital politics -, they combine romance, comedy and corruption in similar ways. Both dramas establish a motive of revenge against politicians that wronged their parents, although it takes a slightly different shape in Dr. Stranger as North Korea's involvement is higher than in City Hunter. Both dramas foreshadow twists that are about to come that keep the viewer hooked. Even the plot twists themselves are partially similar in nature and the romance progression shows similarities too, with both dramas having this sort of archetypical can-but-cannot-be romance structure, just that Dr. Stranger has a more prominant 2nd lead.
Even if the genres are different I would definitely recommend watching these two as a set.
Even if the genres are different I would definitely recommend watching these two as a set.