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It is hard to answer your question. The MBA is an academic degree, typically requiring two years of study. The CS is a professional designation requiring about one year of study and a professional examination. The emphasis is on corporate governance, working closely with boards of directors, and liaison between the corporation, government, and shareholders. The CS studies corporate law, accounting, finance, management, economics, and information technology. The MBA studies those subjects plus marketing, production, statistics, strategy, policy and other business related courses. The MBA emphasizes preparing students for management positions in any level of a business, up to CEO. It appears that an MBA student could structure study in the MBA program to get the necessary background to become corporate secretary while at the same time getting a degree that has more acceptance throughout the world, whereas the company secretary position is limited primarily to India where there are legal requirements to have a person designated as secretary. Of course, all corporation have a corporate secretary even without the legal requirement, but they don't have to have a person specifically trained for the position. Clearly the scope of an MBA is broader than the CS, but that does not mean that the CS is not a valuable position to attain.
MBA programs require a bachelors degree prior to admission, which appears is not required for admission to a CS school. Most MBA programs prefer students with 2-3 years work experience after the first degree, but many accept students right out of college if they have good grades and a high GMAT score. Some MBA programs are designed specifically for new college graduates without work experience.
No one should consider an MBA program without consulting the Official MBA Guide. It's a comprehensive free public service with more than 2,000 MBA programs listed worldwide. It allows you to search for programs by location (US, Europe, Far East, etc.), by concentration (finance, marketing, aviation management, health management, accounting, etc.), by type of program (full-time, distance learning, part-time, executive, and accelerated), and by listing your own criteria and preferences to get a list of universities that satisfy your needs. Schools report their accreditation status, tuition cost, number of students, class sizes, program length, and a lot of other data.