Hi there. 

If the only deciding factor is the package and as you have mentioned that the difference is not too much then by all means you should stay in Mumbai. 

Staying near your home will be better because you will have all facilities of food and shelter and the care of your parents. Moreover, you will be able to save a lot of your time if you stay near to your home. 

If you go to live in a completely new city, it will bring its own challenges. From finding a house to food, your basic necessities would start stressing you out and you might become homesick and your career would be affected because of all this. 

Think peacefully and then choose wisely. 

The nearer to home, the better. 

Hope this helps .

All the best!