They are both dramas centred around family and the struggles they face. The characters are very realistic and the plot is very grounded. It's easy to relate to these stories.
I you liked the relationship of Jiang Lin and Li Bing, or the whole drama with Li Bings family, you will enjoy this drama. Both dramas show the relationships between different members of a family, showing the hardships of adolescence in a dysfunctional family and the the strong friendships that are created over the years.
The settings of both dramas is around the same time period: Romance of Our Parents before and after the Cultural Revolution, and Dear Parents right after the Cultural Revolution. The parents of both dramas are intelligent, humorous and very much in love with each other. They go through all the ups and downs together, taking care of their children, ensuring their bright future paths, and solving all the internal family conflicts.