Better college in what respect? Is it for engineering or any other domain? If you are looking for your choices for Engineering, IIT Mandi is a way better option. Answers to this question depend on various parameters.
Amity Noida:
If you are fond of living in a metro city, then Amity Noida would be a better option to choose. The college itself is reputed and you will get that metro city culture.
IIT Mandi:
On academic grounds IIT Mandi is unbeatable.
Overall, you will never regret your decision to be a part of IIT Mandi if you are not particularly fond of metro- city life.
You must note that all this was for a Science and Engineering program. For non-scientific discipline, Amity Noida is better as IIT Mandi does not offer non-scientific courses. Overall you will see that both the colleges have their own reputation. So, you have to make your own choice based upon your priorities