Hello

AIIMS PG admissions are conducted in two sessions: January session and July session.
AIIMS PG exam for the January session 2020 has been conducted on November 17, 2019 for which counselling process will begin from the first week of December.
Exam for the July session is conducted in the first week of May.

NEET PG 2020 exam is scheduled to be conducted on January 5, 2020 and counseling for admission will start from the second week of March 2020 (tentatively). Admission process is concluded till the last week of May.

NEET PG and AIIMS PG both are separate exams. I would suggest that if you get a seat through NEET PG exam then you should not leave that seat.

Check the counselling dates of both the exams and then you should decide accordingly.

Good Luck!