Full Time MBA

Yes, you can do Both M.Com and MBA degree together if you will do one degree from regular University and another degree from distance university. You cannot do both degrees together with regular University. Also, you cannot do two degrees together from one university at a time. Yes, but you can do two degrees together in Distance education.
If you want to give more preference to MBA, then you can do MBA from regular University. You should do MBA through full Time course. M.Com is general Commerce degree, so you can do it from distance Education. The value of M.Com through distance education is same as Regular.
You should do MBA Full Time course and M.Com Part time course. You have to get admission in IGNOU in M.Com and go for CAT/MAT/XAT entrance test for MBA. In that case, you can get both degrees together in same time and your MBA and M.Com both degrees are valuable.

The cohort at IIMs and NUS is very different in terms of diversity and experience. IIMs have almost half of their cohorts fresh out of college whereas NUS has most of the participants who have reasonable work experience. Singapore being a finance hub attracts an extraordinary exposure in term of learning which IIMs and most top B-Schools in India cannot. Also, the median CTC that is offered at NUS is way higher than that at IIMs. If we see the course fee, the MBA from NUS costs around 40-50L INR whereas the fee for the full-time MBA from IIM A, B and C costs between Rs 17 to Rs 22 lakhs. The student pedigree at IIMs A/B/C and NUS is equally impressive. CAT percentile of 99 and above and GMAT scores of 720 and above ensure only the top minds enter.
The global MBA experience, in my opinion, is what makes NUS slightly better but if someone wants to pursue MBA without much experience, IIMs are an excellent option.