I believe at an EWS Rank of 294, you have fair chances in securing either if the two institutes.

However, IMS BHU is a much older institute with excellent infrastructure, faculty and hospital facilities, campus culture and provides quality medical education. Even if you have to let go of the AIIMS Brand, IMS BHU will be worth the decision.

Do keep a check on the Government Medical Counselling Dates and Procedure. For more information and College prediction do follow the link below

https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer