Depends which branch you have specialized in your Engineering. Civil, Mechanical, Information Technology or Computer science, all branches have their own pluses and minuses for job openings.
Hard reality is that Engineers from top institutes carry on with research or end up in teaching but others opt out for seeking jobs in corporate.
MBA with Engineering degree is positively perfect combination for a job of logistics & supply chain management. Engineers do have edge for analytical understanding of job requirement.
IIMs and other top institutes do get many engineers as their students. Engineers find at least two sections of CAT i.e. Quant and DI sections to score easily because of their DNA of Engineering.
Engineers also get better salary prospects in FMCG companies as compared to core engineering companies. With this market trend even big software companies are also started preferring for Engineers with MBA degree and that too with very attractive pay packages.