Hi there,
It depends on the circumstance and the school.
Unlike Round 3 - which is generally known to have the least number of spaces (although even this is a myth; some schools - especially those outside the top ten - actually admit the same number of students in Round 3 as prior rounds), R1 and R2 are generally considered equal. That said - this can change year to year because there are a certain number of spaces in each round; the more students that apply in R1, the harder R1 becomes as schools will often waitlist a candidate to see who is applying Round 2.
That said - apply when you are ready. A good application sent at the right time is more important than the Round it is submitted. If you think you may get a promotion, have the opportunity to work on a really interesting project, get a better GMAT score, take a course to make up for a poor GPA, etc. than wait. If you don't think your essays are quite there yet - wait. The quality of the application is far more important than timing.
The two exceptions are early decision (binding so often a better chance of admission) or rolling admissions at Columbia. It is a fairly well-known fact that the earlier you apply to CBS, the better your chances.
Overall I advise candidates to look at their applications, look at what they can achieve between R1 and R2, and look at their schedules. Submit when you can submit your best work. This far exceeds the importance of the round.
Pamela
p.s. Additionally, while not statistically significant there are published facts on the percentage of the class admitted each round for each school.