Let me answer your question by describing them individually. 

MHA:

Duration: two full academic years divided into four semesters.

Program description: The MHA programme aims to prepare a candidate to assume the responsibilities of a hospital administrator or executive in a government or corporate or any other hospital. An important aspect of a hospital administrator’s life is to be able to act as a successful intermediary between governing boards, medical staff, and department heads and integrate the activities of all departments so they function smoothly as a whole. With a successful MHA and your consistent performance that you might be able to showcase, you might be able to reach upto the position of CEO. 

Job profile: Strong leadership abilities, creativity, social responsibility and inter-personal skills in high-stress situations. 

Salary Structure: An entry-level position as Assistant Medical Superintendent could command between Rs. 40,000-50,000 and then go up to Rs. 50,000-55,000 as Deputy Medical Superintendents, then close to Rs. 1 Lakh as Medical Superintendent. As your career progresses you could reach the level of an MD and earn between Rs. 1.5-2 lakhs per month.  Perks include HRA, Medical, transportation and accommodation. Medical professionals who become administrators can earn a slightly higher package.

Institutions offering MHA course:

*AIIMS

*Armed Forces Medical College,  Pune

*Kasturba Medical College, Manipal

*FMS, New Delhi 

*The National Institute of Health and Family Welfare, New Delhi

MBA:

This is also a two year program or might be a one year program (in ISB, Hyderabad) 

MBA is a comprehensive course that will open a gamut of opportunities in front of you ranging from investment banking to other financial arenas, from sales to marketing, from operations to IT, from human resource management to consulting including pharmacy which happens to be your domain.

When MHA on one hand will bind you by limits into your pharmaceutical zone, MBA will give you wide range of opportunities. 

You might end up landing into a different kind of job and domain, May be out of your comfort zone but with a whole new learning experience and different salary package too. 

One point of importance is that, a position that you might get after pursuing MHA, the same position you can get even after completion of your MBA program. Added to that MBA will open enormous opportunities for you in future to try out new sectors. 

Exams for MBA: CAT, XAT, CMAT, GMAT, MAT

Institutions for MBA:

*IIM (Indian Institute of Management) 

* XLRI, Jamshedpur

*JBIMS, Mumbai 

*MDI, Gurgaon 

*S. P Jain Institute of Management and Research, Mumbai 

*IMT, Ghaziabad 

*T A Pai Management Institute (Manipal) 

And many more. 

Hope this helps you. Take a wise decision. Choice in the end must satisfy you.