Similar characters. We have an older, more cynical and serious character that does not hold back to fight for his justice, while the younger one is trying to fight for the "good" of humanity. Both revolve around the law and both evolve around similar concepts. Generally both dramas give off very similar vibes.
What is justified when it comes to justice? Both dramas thematize this question. Both have criminals and the question of how far the legal system should go in order to punish them. Both demonstrate good and evil, morals and fairness. Both main characters go controversial ways and make you question your own standpoint on how far one can go for it to be too far.
Power struggles to rule over Daehan Minguk (South Korea) presenting the main issue in both the dramas, the main in CoS is driven by ambition while those in TDJ are driven by revenge and righteousness. The push and pull tactics of politics, money and power trips are exhilaratingly displayed in both the masterpieces.