hello sivarama,

hope you are doing well,now coming to your question

Yes, BHMS and BAMS is included in AI quota seat through NEET. Plus aggregate marks in 12th for General category should be 50% and for OBC/SC/ST should be 45% and PH should be 40%. yes, there is all India counseling for it

BAMS, of-course has the greater potential than BHMS. Ayurveda is getting an edge over allopathy etc.
When it comes to graduation in Ayurvedic medical science, the students will be taught entire subjects that involve knowledge of this field, inclusive of modern science. In this course, the study load for students will be more as compared to MBBS and BHMS.

In BHMS, students will learn only some areas of modern science, while the other subjects will be mainly focusing on homeopathic medicines. When it comes to study load, it will be equal to MBBS or even slightly more as well. Here, it will be difficult for students to remember different medicines for different conditions as per homeopathic material medical.

please go through the following link for more details

https://medicine.careers360.com/articles/bams-vs-bhms

hope this will help you a lot

thank you