R1 or R2, there really isn't much difference. Last round (whether that is R3 or R4) is difficult like others have mentioned in the forum. But in the first 2 rounds, the only difference is the number (1 and 2) after the word "Round".
Multiple rounds are available for the benefit of the bschool, not the applicants. It allows the admissions officers to manage the app volume, and as a result, allow them to do their job better. (Can you imagine if there was only one round?)
If you ask any adcom if there is a difference between R1 and R2, they will tell you the same thing. Believe it. They have no reason to lie to you.
The only benefit (that I can think of right now) to apply early, may be scholarship related purposes. Money may be available to the admits of earlier rounds in some bschools. There are scholarships offered towards the end of the app cycle, but there are also specific scholarships (usually named after an alumni funding the scholarship) that can only be offered to admits with specific background. If an admit from R1 accepts that scholarship and commits to the school, then R2 admit with similar background who may qualify for that scholarship may miss out since it is no longer available to him or her.
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