Does black tea have the highest level of caffeine? If so, why?
Rate Tea tells us this is a myth:


  Many tea companies, and even some reputable entities such as the U.S.
  Department of Agriculture, have made misleading generalizations about
  the caffeine content of broad classes of tea. It is a widespread myth
  that black tea contains more caffeine than green tea, and another myth
  that white tea contains the least caffeine of all teas.


They indicate that brewing method is the main determiner of caffeine levels in the brewed tea.

The source article goes on to cite various credible scientific sources, which raise the credibility of this assertion.  Unfortunately, most of their links have gone bad, which makes it harder to check the background science.

This caffeine level table from Mayo Clinic does indicate slightly different levels, but that is likely to be a result of different brewing details across tea types rather than fundamental to the tea plant itself.