Either way (birth-control pill or tampon) will work. I'm a scuba diver and I've done both for dive vacations. I prefer using tampon because it's a more nature way. Just remember you can always choose not to dive or dive less if you not feeling well.
If you choose birth-control pill, you should talk to your doctor and may need to start it 1-2 months ahead of your vacation. You might still spot even if you take the pill on time. And there might be some side effects.