See if you apply for both JEE and NEET then you will have a broader perspective to be opened for you both in Engineering as well as Medical fields. Although studying this in parallel can be intermediating. Now if you have the main interest in Engineering then you should focus more on JEE and less on NEET. As you prepare for JEE then your physics and Chemistry will be stronger than most of the students preparing only for NEET. So you will get some advantage that way. But if you feel Medical is the field you want to go for and just to be safe you want to appear for any engineering entrance then I would say better than JEE you go for state engineering entrances and focus more on NEET. The state engineering entrances are relatively easier to JEE so if you by chance not get NEET then also you will have very high chance to get in state engineering colleges.

**This is entirely dependent on my point of view. It may differ with other but I have provided the logic and I hope you will understand what I want to say.

To know more about JEE visit the link below:

https://engineering.careers360.com/exams/jee-main

To know more about NEET visit the link below:

https://medicine.careers360.com/exams/neet

For top 10 engineering entrances visit the link below:

https://engineering.careers360.com/articles/top-engineering-entrance-exams-in-india

I hope this answer helps. All the very best for your future endeavors!