You can find some of the differences discussed here - https://www.quora.com/Is-ISB-Hyderabad-better-than-IIM
Both IIM Bangalore and ISB Hyderabad are premium and very strong institutions to do an MBA from. IIM Bangalore is one of the prestigious "IIM" institutes (and one of the top 3 consistently) and has been there for many years. It is a first choice for many aspirants and has seen a legacy of alumni who are today leaders in the industry. ISB is relatively newer, but has also built up a very strong reputation over the years. The IIM course is a 2 year program in Management, where you do general subjects in Year 1, and then choose your specialization in Year 2 (e.g Marketing) and pursue subjects of your specialization. At the end of the second year, students typically get placed in a job from a top organization. ISB used to be a one year course, but may have moved now to a 2 year course. Both are very strong options, but my vote will go for IIM Bangalore given its long heritage and reputation in the industry.
Do your research on both before you make your choice. As both are top notch, you will be choosing between the best, so you're at a sweet spot right now.
Good Question. Both the institutes are very good. You can't go wrong choosing either. A lot depends on the course/specialization you want to pursue. So, my suggestion would be to compare based on the specialization of your choice. The next thing would be the cost of the course. ISB is generally a bit more heavier on the wallet compared to IIM. Also, ISB is generally preferred by professionals who already have 5 years of working experience.
Hope my answer helps. All the best!