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.

There are two factors that matter: the duration of steeping, and to a lesser extent, which portions of the tea plant are used.

In Japan, most people brew Japanese green tea for a matter of seconds, unless they are brewing a tea like gyokuro that has better results with a low-temperature steeping. Oolongs also tend to have a shorter infusion time than black teas if prepared by oolong enthusiasts, though generally longer than green tea. In contrast, most Americans and Europeans steep black teas for on the order of 1-5 minutes, depending on whether they are using a typical dusty teabag or a tea with mostly unbroken leaves. In practice, these brewing differences make up the largest difference in caffeine content.

However, there are certain varieties of teas which have a lower content mostly because they use different parts of the tea plant. Kukicha, for example, tends to have a lower caffeine content even with a longer infusion time because it consists mainly of leaf stems and twigs, which apparently have lower caffeine content than the leaves.

There seems to be no well-understood correlation between the level of caffeine in tea and the type, processing, or brewing. Actual data seems hard to get hold of, because measuring the caffeine content of a cup of tea requires expensive laboratory equipment.

Tea: history, terroirs, varieties by Gascoyne, Marchand, Desharnais and Americi (Firefly Books, 2011, translated from the 2009 French original) reports on the caffeine concentration of 35 different teas, measured by liquid chromatography. 5g of tea was brewed using temperature appropriate for the type of tea. The brewing times all seem quite long (3.5 to 6 minutes). The results are all over the place: 58mg of caffeine per cup for a First Flush Darjeeling (nominally black), 50mg for the (green) Xue Ya and Tai Ping Hou Kui, 49mg for a Bai Hao wulong, 48mg for a (green) Sencha, down to 12mg for a Tie Guan Yin wulong and another Sencha, with Yerba mate (not a tea) at 18mg, an Assam (black) at 22mg, and a white "Bai Mu Dan Wang" at 39mg.

The top caffeine content reported was actually an outlier. This was 126mg, using only 1.5g of Matcha that had been infused for only 30 seconds at 75°C (167°F). Perhaps this indicates that powdered tea has more caffeine than other types, but I would hesitate to draw any other conclusions without a lot of further study.