Hello,
Well my friend you have asked a question which has dead end. In these positions, the focus shifts from technical tasks to administrative ones. Managers develop plans and schedules for reaching technical goals, such as new product development. ... However, many managers also have a master's degree in engineering management, technology management or business administration.

You can opt for management if have interest in managerial skills like motivation, leadership, business, etc.
Or else go for engineering if you have interest for technical field.

I wish you all the best.
Cheers !!

You are comparing between engineering and management.

Both are different fields and have different sets of educational requirement like a commerce students cannot apply for engineering whereas an engineer can apply for MBA or management studies.

First you will have to check whether you are eligible to apply or not.
Second you need to recognize your interest and career.
You will have to decide which field of interest suits you and what you want to do in future.
After engineering you can go in the following careers:
(depends upon the specialization you choose)

Electrical engineering
Petroleum engineering
Computer engineering
Aerospace engineering and more.

After MBA, following can be your career into,
Marketing profile
Finance profile
Hr Profile
Banking
Tourism
hospitality and many more.

Based on the above you will have to decide your interest.
Salary packages in both are good as it also depends upon your profile and designation as well.

Good luck!