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.