This is my personal opinion, but they're much better and more human and three-dimensional.
In the movie they're generic suffering parents, which is okay because they don't need to be anything more, but in the show they're considerably more fleshed out in a way that feels natural.
Rapunzel's father isn't predicable in the way they portray it, like, he isn't all good or all bad, his deep hurt makes him make mistakes. He's overprotective but it's not played for laughs, it's serious. He has guards follow the daughter around and he even closes her in a tower himself.
He keeps secrets and ignores problems in hope that this will mean Rapunzel doesn't get hurt. He only wants the best though and he'll learn from his mistakes.
At the same time he wants to belong. He's not just a king, he wants to get along and be included by Eugene and his friend Lance, he tries but mostly fails.
As for the mother, she feels heavy in her heart all the time that she lost where she couldn't spend it with her daughter.
She desperately wants to be there for her, be the mother she wished she could've been those 18 years.
She'll show a side quite like Rapunzel, and this'll play a role in how understanding she is. She knows Rapunzel longs for freedom and supports that desire, despite this meaning that they won't be together.
I really like what they did.