Same adorable lead actress, Both are fun romantic comedies with lead males that despite having a complicated and rocky relationship start with the spunky lead actress they fall for her. There is an interesting dynamic in both that put the actress in a position of power over the male leads early on. There is also a time in each that the lead male seems a bit emotionally dependent on the leading lady. the main difference is that HL deals with gangsters and DIL deals with bad marriages.
In both dramas, it feels like the female lead is really underappreciated for everything she does. They also both carry similar themes (lawyers, personal issues) and have romances which, although light at a first glance, have a deeper root. If you liked Prosecutor Princess, then Divorce Lawyer In Love might be even better, as the secondary characters also have better and deeper development than in PP.