Being forced to answer this question because of multiple requests. Honestly there is no clear answer. If I am from Karnataka and I got the same branch in both, I will take RVCE. However even if in Karnataka if I am in say the northern part like Hasan; Goa might be closer and my choice might change.
From whatever I see and hear, I will think that if you got CSE in both you are certainly in the right league. For other branches I am unable to compare but I know that the quality of intake into RVCE for non CSE/ISE/ECE branches drops just a bit. BITS is more a big hype story. So there are many who consider it big stuff. I personally dont agree. Infact BITS Placement Department is treated better by many companies but in the end the selection is similar. So there is no point in arguing.