Both Miranda House and LSR are reputed colleges of DU, and have made significant contributions to women’s education in the country. You should choose one of these two colleges, based on the course of your choice. Miranda House is known for its science courses and LSR is the best college for arts.
MH and LSR offer unique campus life. If you want to experience the much-talked-about DU campus life, choose MH. You can gate-crash into fests and events of other colleges of DU. LSR is more posh, infrastructure-wise, and offers an enviable campus experience.
Both are very good institutes. As some of my friends studied in both Miranda House (MH) and LSR, I might be able to give you a basic idea about them.
Overall, both these institutes are equally good and you will see yourself grow and change as a person intellectually.