Both Christ University and St. Joseph College Bangalore are reputed. In terms of quality of education, the former is a little ahead. However, economically St. Joseph is a better choice. As the course fees are more affordable. But both will provide you with decent opportunities. Christ offers better foreign exposure in terms of foreign lecturers and professors. 

Christ is also quite strict regarding dress codes and rules on campus. Accommodation around Christ is cheaper compared to St. Joseph. Since St. Joseph is located in central Bangalore. 

You can choose either of these two institutions, according to your convenience