MBA/PGDM

https://www.shiksha.com/mba/articles/top-10-institutes-for-distance-correspondence-mba-blogId-6301
Please click on the above link and kindly go through the list of best distance MBA colleges/universities in India.

According to me, both are good but Amity is better than ABBS as both provide the best knowledge but would I suggest you to go with Amity. You can choose according to your preferred location.
All the best!

If you are asking about Bangalore Institute of management studies (BIMS), then I would say ABBS is better in terms of placement as well as academic exposure.

IIMs do not offer MBA or PGDM in Tourism and Hotel Management courses.

https://www.shiksha.com/mba/colleges/distance-correspondence-mba-colleges-delhi-ncr
Please click the link above and kindly go through the list of MBA colleges that provides distance MBA in Delhi NCR.

Approximately 3 Lacs per annum. This was the fee structure last year. There might be an increase in the fee this year, check it out once with the university.

ABBS is ranked top 6 business school in Bangalore and also Acharya Bangalore B-School has always ranked among the top 1% of the best B-Schools in India.

If you are doing BBA+MBA in a good university/college, that provides good business education, has good faculties, provides exposure, place students at good companies with a good package, it's worth doing the integrated one. Example- IIM-Indore provides integrated MBA. But if you get into not so good BBA college, it will be better to give CAT exam, get a good percentile and get into a good MBA college.