I don't work in a clinic, but I can address what our delivering docs recommend. If you have a stable, compliant patient, it's the Pill. For others who might have issues getting refills or remembering to take pills, Mirena and Implanon seem to be the choices. Depo Provera for the in-between patients. You also see Nuva Ring and the patch occasionally.
I am new to the ob/gyn office setting so its too early for me to say "what I see the most given" is.....but we still do implanon. We only have 1 provider trained to do it so I don't see it a ton (we are a huge practice with 7 providers). The majority of the pts that get it are usually unable to tolerate the combination pills. They use it as a "last resort".