Which would be better: Taking admission in PGDIE in NITIE, Mumbai through GATE or join a PSU and do an executive MBA from a good institute after about 7 years?

A friend of mine worked with a PSU for some time and then appeared for the GATE exam and joined NITIE PGDIE. Leaving the PSU and choosing something else is a personal decision. It depends on your perspective.

In your case, joining after 7 years seems like a long-term plan. You can end up not joining any course after 7 years. So, make sure why you want to join a course after seven years, is it for the degree or salary hike. 

If you are going for it for the degree then it can be done by joining any institute. There’s no need to join NITIE specifically. If you are doing it for the salary hike then too, you can join any institute. There is no differentiation based on which institute you are from, in PSUs. All the students having a Master’s degree are treated equally. Then there are options for joining private institutions such as NITIE which is a good option too.