Microeconomics, Mathematical Economics, Game Theory - ISI
Econometrics, Macroeconomics, and a wide variety of other topics that you will only get at DSE (I mention this because you are unsure of exactly what it is you like/want to do later on) - DSE
Essentially, depth in a relatively focused area is ISI. Breadth across everything Economics is DSE.
To be very honest, given the way you described the institutions you would like to work for, I would say DSE suits you better. That is because of two reasons-
1. The alumni network DSE would have at places like the world bank, asian development bank, ministry of finance, RBI, and companies like CRISIL, etc. ISI has just no chance of overtaking DSE any time soon in this regard. It goes without saying that alumni goes a long way towards getting jobs at such institutions
2. The places that you want to work for, require focus on areas that DSE has a clear relative advantage in. Macroeconomics is the perfect case in point. RBI, WB and ADB won't really be doing game theory on a regular basis. They require exceptional knowledge of International Trade, Growth and the Macroeonomy. DSE is better than ISI in these fields.