The answer will differ depending on people and their professions but these two cities have advantages and disadvantages that will help you make the right choice. Chennai is known for its automobile industry but if you are looking for work in the other fields, it is best that you consider Mumbai especially since it has commercial and business opportunities.
This will depend on your specialty. Do you need work that is related to boats and such? Mumbai has a port and will provide more chances for you. Aside from earning more, you need to think about the cost of living in these places plus the other things that they can offer like food and vacation spots.