Aeronautical Engineering

This is a tough question. But you should know that both the fields have different end goals for a student, but can overlap in certain situations. Mechanical Engineering is a core branch and has been a favourite of students who wish to get into the aerospace and aeronautical industry. The reason is that it gives you a broader knowledge in the mechanical domain, which includes the aerospace domain as well. Another reason is that organizations in India, whether Public or Private, prefer mechanical engineers for their broad spectrum of knowledge. Aerospace engineering focuses more on the aerospace and aeronautics industry and is an apt course for people who wish to mostly work in the private sector. It can also pave the way for a higher education abroad and then opportunities to work in international organizations (such as NASA, Airbus, Boeing, etc.).
You can go for aeronautical engineering as it is more specialised.