An 8 fl oz cup of brewed coffee carries 95 mg of caffeine, 32 mg more than a single shot of espresso (1 fl oz, 63 mg). Ounce for ounce it flips: Espresso is far more concentrated at 63.0 mg/oz, against 11.0 mg/oz for brewed coffee.

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 serving, side by side

Brewed coffee, 8 fl oz (237 ml) 95 mg
Espresso, Single shot, 1 fl oz (30 ml) 63 mg

Sources

Drink Serving Caffeine Source
Brewed coffee 8 fl oz (237 ml) 95 mg USDA FoodData Central, coffee brewed with tap waterSource
Espresso Single shot, 1 fl oz (30 ml) 63 mg USDA FoodData Central, espresso, restaurant-preparedSource