I split my applications between R1 and R2. Most admissions officers say that R1 and R2 are pretty much the same. Stanford is the only school I can think of that explicitly encourages applicants to apply in R1.
People have different reasons for splitting up their apps between R1 and R2. The most common are:
1) To lessen the workload for any particular round. Even putting one application together takes a lot of work and while it usually takes less effort to complete future applications they are all a time intensive project. Many people split the rounds so as not to wear themselves or their recommenders out.
2) Applications get better as you go. Each subsequent application is better than the one before it (up to a point where you reach diminishing returns). Many people save their dream school for R2 in order to capitalize on the benefit of having previous applications and possibly interviews under their belt.
3) Splitting rounds can offer a second chance. Some people like to test the waters in R1 and put out applications to a safety school as well as one or two reach schools. If R1 ends with 0 admits (or worse 0 interviews) there is enough time between R1 and R2 to regroup and hit the next batch of schools. For example, let's say a person has a borderline GMAT score. The R1 picture starts to shape up about 3-4 weeks after submission deadlines as interview invites roll in. If by November R1 is looking like a bust then there's still time for a GMAT retake and to hit 1-3 more applications in time for R2 deadlines in January.
Splitting up rounds is a personal choice. If you're planning to only apply to 3-4 schools it's doable in one round. If you feel the need to apply to 5+ schools and haven't started working on apps now (like right, right now), then it may be best to spread the work between rounds. Be mindful that if you do apply in R1, get accepted, and still want to shoot for additional schools in R2 then you will likely have to pay a deposit to your R1 school BEFORE you know if you've been accepted anywhere in R2. Deposit and decision days can be weeks apart so I do not recommend choosing this route with the expectation that you can get an extension (especially in R1 since that yield impacts R2 decisions). Hope this helps clarify things somewhat.