USA

Hello, You should check the websites for Stanford B school & Indian B school to see & compare the curriculum yourself & you would be able to make the difference, being a BBA student yourself. It really depends on the peer group & class cohort you get to learn the theory with in Stanford or an Indian Private college as the students of the class only contribute to live, learn & grow together which contributes to difference in learning between a foreign University & an Indian college as the students from different parts of the world & share globally rich experience in a foreign university.
For an MBA from a Stanford equivalent university, you need a US equivalent Undergrad degree, strong GMAT & TOEFL/IELTS scores, diverse extracurricular skills, Letter of references, Essays & a timely submitted application from India.

MBA has a predefined syllabus provided by the universities and the syllabus changes seldom.
PGDM is offered by an autonomous institution and the institutes make their own syllabuses according to the market trends.
Both the courses have their own values and carry their own prospects. You will not face any difficulty during the time of getting job if you have any of these degrees, But MBA is the name that everyone knows and a few don't even know that PGDM exists. But I can assure you that both are equivalent with respect to superiority.
Personally I prefer MBA, everyone has their own choice. But please choose your specialization according to what you want to become in your life. Don't take your decisions with affect from your friends, community, market conditions, etc.