Hey,
Yes, you cannot give both the exams on the same date at the same time, so you should go with your first priority.
NATA (National aptitude test for architecture) exam is for getting admission into 5-year B.arch course and as you said that your AMUEE exam is for B.Tech.
So, choose it wisely on the basis of your *interest* and *priority*. If you want to do B.Arch then go for NATA and if you want to do B.tech then go for AMUEEE.

All the best!