It all started with Big 6 (Coopers & Lybrand and Aruther Anderson, I suppose existed earlier as part of the group), after they left no-one thought of adding another firm to keep it Big 6 of even change to Big 10. Other firms in the top list include, Grand Thornton, Baker Telly, Moore Stephens, Pannel Kerr Forster, Horwath, etc.
On the Indian side, the list include, Ferguson, Haribhakthi, NM Raiji, SR Batliboi, etc (apologies if I omitted any other as I am just recollecting my memory).
To answer your question, ICAI President is not correct by saying Big 2.
You are lucky that you are selected in both and your problem is to select one (where the problem with most of other students are that they cant get into any). My advise (yes it is mine only) would be to go for KPMG. Their partner Mr. Natraj Ramkrishna is the one under who I got training and I liked him to be a very people person.