SJMSOM at IIT B was founded in 1995, making it a relatively newer institution. But for a couple of years now, it has been making headlines because of some really outstanding profiles that were provided. Its core competencies are operations and supply chain management. There is no doubt that IIT B is the best choice if you want to work as a product manager. IIT B also has a beautiful campus with excellent facilities.

Additionally, it would give you the opportunity to take part in MOOD-I, the most significant cultural festival in all of Asia, which is held at IIT Bombay. With the well-known tech fests, there is another opportunity for you to participate. Furthermore, there are benefits to living in Mumbai. For guest lectures, the majority of the industry experts live nearby and are easily reachable. 

IIM Lucknow was founded in 1984, so it has 11 batches more alumni than IIT B, resulting in approximately 3300 more alumni (considering 300 students per batch on average). It is also the fourth oldest IIM, following A, B, and C. You will gain a lot more industry experience, which will assist you in deciding what you truly want to do. In addition, IIM L offers better opportunities in Sales & Marketing, Consultancy, and BFSI than SJMSOM. Furthermore, you will be networking with a large number of students from all over the country and forming lifelong friendships. Furthermore, the IIM tag for a managerial position has an advantage over the IIT tag, which is still developing.

It would be fine if you went to IIM L, SJMSOM, or any other B school a few years later. When you switch from the first company you get after your placements, the new recruiters will be more interested in your work than in the college you attended. And the impact of your college's name gradually fades. What remains are the lessons you've learned and the memories you've made over the last two years.