Having friends studying in both the institutions, I can say that both are good. If you see, Bharati Vidyapeeth is quite an old institute as compared to DY Patil.

Moreover, Bharati Vidyapeeth is good for applied arts; which is situated in main Pune city. It also has good infrastructure and facilities. On the other hand, DY Patil is famous for engineering and technology which is situated in Akurdi and Pimpri.

The following table gives a brief overview of the institutes:

If you want to have a good atmosphere, good facilities, experienced teachers & prestigious institutions go for Bharati Vidyapeeth. DY Patil is also a good option but both have minor differences.