What you're referring to is the long-term vs the short-term capital gains tax rate, which depends on the income bracket you fall into. For residents, the long-term rates can be 0%, 15%, or 20%. The short-term rates are treated the same as normal income.
Non-residents are subject to a withholding tax of 30% on dividends, but you get 15% because of a tax treaty (see here last column). Additionally, you still get hit by the 30% tax, lowered to 15% by treaty, on capital gains since its FDAP that is not Effectively Connected Income to US businesses and trade, which is explicitly mentioned here.
So, simply put, you get hit by a 15% tax from the India-US tax treaty on everything.
Edit: actually, I'm not sure how living in the UAE changes things. You will be living under 3 tax regimes: India, UAE, and US, and I can't even fathom how they begin to interact with each other. I'm semi-confident that you still get 15% from the treaty with India, since the UAE shouldn't be taxing you on foreign income (seeing as the US in unique in its insistence on taxing all the money of its residents). I'm not very confident in my answer, so if anybody knows more feel free to correct me.