Among the two institutes mentioned, St.Xavier College, Mumbai is better for a BA in psychology. 

The table below will give you a brief overview of the two colleges.

Comparison: 

Both the institutes provide good learning opportunities, but the difference is St. Xavier is autonomous and hence better.

• As St. Xaviers is autonomous, it can update the syllabus anytime, if needed. While Jai Hind is affiliated with MU and follows the same syllabus as MU. Which may not be updated. 
• Xavier’s also conducts its own examinations. So any problem caused in the result published by MU will not affect the students of Xaviers. 
• Like any other autonomous institute, Xaviers also publishes its results first. So, students get the first preference for a job. 
• While containing a degree from MU through Jai Hind is quite convenient since university and college will both have a set of mark sheets.

From the academic point of view, St. Xaviers College is better than Jai Hind College Mumbai.