Hello Kalavathi, Greetings!
Let me tell you that both the branches are very good.
So, your choice between branches should depend upon the career foresee yourself.
In aerospace engineering, you learn about professional design, building, testing and maintenance of civil aircrafts, missiles and space shuttles.
Aeronautical engineering is more like specialisation where you learn about designing and testing of aircrafts such as aeroplanes and helicopters.
Some of the top colleges to pursue above carrers are - 
IIT Bombay
IIT Madras
IIT Karagpur
IIT Kanpur
IIST Tiruvanatapuram
Best of luck.