An 8 fl oz cup of green tea, brewed has 29 mg of caffeine. The same size cup of black tea, brewed has 47 mg - 18 mg more. Both come from the same plant; the difference comes down to how the leaves are processed and oxidized, not a different source of caffeine.

Figures come from USDA FoodData Central; see the source link in the table below. Add either one to the caffeine calculator to see how it fits your personal daily limit.

Standard cup, side by side

Green tea, brewed, 8 fl oz (237 ml) 29 mg
Black tea, brewed, 8 fl oz (237 ml) 47 mg

Sources

Drink Serving Caffeine Source
Black tea, brewed 8 fl oz (237 ml) 47 mg USDA FoodData Central, black tea brewed with tap waterSource
Green tea, brewed 8 fl oz (237 ml) 29 mg USDA FoodData Central, green tea, brewedSource