AIEEE and JEE are the same in the sense that these are exams that are needed so that the candidates will be able to study engineering courses in certain institutes. Take note that the institutes wherein the students can enter can be government institutes or private institutes. IIT is considered to be more prestigious because this is harder to take. In order for students to be qualified to take this, they would need to take two types of JEEs available.
IIT is considered to be tougher as compared to the AIEEE. These two tests also have different scopes. You can expect that the AIEEE will be focused on the demand, the speed, and accuracy of the projects that need to be done while the IIT will be focused on the different building concepts that are available.