Both have court room Drama.
Both shows have a procedural formula for Legal Cases with an overaching main plot.
Both shows have social commentary and they point out/deal with societal flaws and stereotypes.
Both shows are more focused on the courtroom stories and legal cases instead of romance.

Where it differs is that One Dollar Lawyer has sattire, eccentric lead and a more comedic tone while Miss Hammurabi has a more serious undertone centered on character development.