Aircraft Management Engineering Common Entrance Test (AME CET) is the common entrance test to offer admission in Aircraft Maintainance Engineering Course in India. Student will get admission in Govt. approved AME institutions in India. India is fastest growing aviaition market with several private airlines and coorporations. There are plenty of oportunities available in this field.

JEE is the entrance test to get admission in IITs, NITs and other GFTIs where one can pursue engineering degree of their choice based on rank obtained in the exam. 

Finally it all comes down to you where your interest lies. If you are so much passionate about Aircraft Maintainance then go for AME CET. If you want some engineering degree apart from that then go opt for IITJEE. Several institutions provide course in Aerospace and related fields like IIST and take admission through JEE, you can opt for those if interested.

All the best.