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In My Opinion, market positions for banks are very fluid in APAC and India. You see BBs take the lead one year, then locals, then EBs another year etc. Rothschild is more in prestige and exits I would say on an international level, Jefferies is seen as a rising star.

Despite the small on the ground work force for each, they are both pretty good. I've seen a lot of ex-Rothschild India execs go and run big corps in India, (after reading many annual reports), which is also another added plus.

Jefferies is not even that active in APAC.

Isn't it very very tough to find an IB job in India?  Unless you had multiple options, I'd just take whichever you got.