New Tales of Gisaeng (2011)

It has one of the same characters and actually has some references to the show! New tales is pretty much continuing the characters story from Assorted gems :D

A similar theme of a rich family's son falling in love with a poor girl, and how they try to overcome the difficulties.

Both titles blend modern day Korea with traditional Korean culture. They also both have the rich man/poor woman trope.

Both of these dramas star a female lead with a birth secret, who has a self sacrificial outlook on life. Both lead females are super depressing because their circumstances in life sucks, however these two characters still make you root for them, they are good inherently so you as a viewer wish they would finally find happiness. The day to day dialogues and outdoor events done by all the different characters are similar, both dramas have a slice of life quality to it that you don't see in long running dramas anymore.

it too deals with jealousy obsession the falacy of unconditional love

In both series the main couple meet accidentally many times. The girl even comes to his house invited by one of his family's member.

A poor girl and rich boy fall in love, she is independent and he a bit arrogant plus his parents do not approve of their relationship.

The rich guy who has both the looks and wealth, who seems to have it all on the outside but grows up with family issues falls in love with a girl who is the opposite.

In both dramas male lead and female lead is same...
In both dramas Rich Male lead and Poor female lead...

They have different stories but they are kind of similar. Both are about a girls life and her struggles in life. And how she tries to live a good life after a life turning event. And in both of them the main girl and main guy struggle to be together.

The Empress has a almost similar storyline and main couple as NTOG. Some scenes feel almost mirrored in the beginning. Both have birth secrets and women becoming gisaeng/hostess and men who can't live without them!