Why is that BIT Mesra has not gained as much fame as BITS Pilani though it was setup before BITS, with good infrastructure?

BITS Pilani is located in Rajasthan, which is and used to be a part of India's so-called active north. As a result, BIT Mesra is not preferred by the people of the north, who have better options of IITs and NITs. While some go for the south. It is only an ideal place for Bihar, Bengal, Orisha, Jharkhand, and the neighboring state.

BIT Mesra was ranked 7th by India Today Group Survey, but it remains isolated in terms of fame because students are the biggest marketer for a deemed institution. If you say, “Hey, I am from Bit Mesra,” the likely answer would be, “Is it a subsidiary unit of Bits Pilani?” As BITS Pilani is more reputed. 

Here are a few other reasons why BIT Mesra has not gained much recognition among the students. 

• The kind of behavior carried or promoted among teachers is more akin to a school teacher, so the title professor is unnecessary.
• The management approach at BIT is very bad; there is a lot of paperwork to be done for any minor thing. From the time you enroll until the day you leave the campus you will have to go through many paper works.
• Off campuses are given no value by the main campus, and this is a major reason why BIT is not mentioned with off campuses. Whereas Pilani has four centers that are advertised, in very good condition, and are given true care by the Pilani main campus. This is a major reason why Pillani is more well-known than Mesra. 
• There is no student council or student politics, and no student welfare council composed of fellow students exists or is promoted.
• Apart from these, the governor of Jharkhand, who is only present at convocations, is the chancellor of Mesra, while Pilani is completely managed by the Birlas, with MR Kumar Mangalam Birla as the chairman.
• Another major reason for Pillani's success is the engineering entrance exam pattern. BIT Pilani organizes a separate exam called BIT SAT, whereas BIT Mesra does not take any separate exam.

This all that I have learned through my connections at the institutes. Hope this helps in clearing your doubts.