The only school that specifically encourages people to apply in R1 vs. R2 is Stanford. If you are not applying to Stanford then apply when YOU are ready. If that is in R2 then so be it. I split my applications between R1 (Kellogg) and R2 (Stanford, Booth, Wharton) last year. I got into Kellogg, Booth, and Wharton. I do not think that the round in which I applied made any difference. I submitted my apps when they were ready.
If you think you will have something substantial (promotion, significant EC accomplishment, higher GMAT, completed class) to add to the application after R1 deadlines then wait until R2 to apply. If your application would be the same in either round then pull the trigger and apply in R1. In my opinion the competitiveness of the rounds is equal, albeit in different ways. R1 tends to attract a lot of very strong candidates. These tend to be the people who have their stuff together early because they've been preparing for apps for the last 2 years. R2 has a much higher application volume, but I think it's probably diluted a bit in terms of strength of candidacy. So you have to decide if you want to go up against the proverbial "rock stars" in R1 or take your chances with a larger applicant pool in R2. Hope this helps.