Both dramas are centered around revenge. The glory is about a woman taking revenge on the bullies from her high school days. The devil judge is taking revenge on the powerful people that killed his brother. If you like to watch evil people finally get the karma they deserve, I think you will like both dramas.
Revenge thrillers with strong female leads. In Lady Vengeance, there is a (younger) man who falls for the female lead. The male lead, in The Glory, who is younger also has feelings for the FL. The Glory is about revenge towards bullies while in Lady Vengeance it’s also towards those who have wronged the FL (but not bullying).