This is a very subjective question and it depends on what you're looking for in a school. From an academic standpoint, it would be tough to say one university is unequivocally better than the other.
When it comes to Aerospace Engineering, both MIT and Purdue University have stellar reputations. MIT is consistently ranked as one of the top schools in the world for engineering, while Purdue has a reputation for producing successful aerospace engineers.
In particular, Purdue is known for its Applied Aeronautics Graduate Program. It has a strong emphasis on the fundamental principles of aerospace engineering, and its graduates are well-prepared for careers in aircraft and spacecraft design, development, and operations.
At the same time, MIT is renowned for its research in aerospace engineering. It offers students the chance to work with some of the most advanced technologies, from space exploration to aeronautics. Many MIT students go on to have successful careers in the aerospace industry.
In the end, it comes down to individual preferences. Think about the type of experience you're looking for and which school you think offers the best opportunity to reach your goals. You might even consider looking at other schools that specialize in the same field.
Many universities also have cooperative programs with industry partners that can give you a unique opportunity to learn while developing professional connections. Do some research to see which program best suits your needs.