A 12 fl oz can of Diet Coke has 46 mg of caffeine, 11 mg more than the same size can of Diet Pepsi (35 mg). Neither is a large source of caffeine on its own; the gap matters most if you're counting every milligram closely.

Figures are each company's own published data; 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 can, side by side

Diet Coke, 12 fl oz (355 ml) 46 mg
Diet Pepsi, 12 fl oz (355 ml) 35 mg

Sources

Drink Serving Caffeine Source
Diet Coke 12 fl oz (355 ml) 46 mg The Coca-Cola Company, ingredients FAQSource
Diet Pepsi 12 fl oz (355 ml) 35 mg PepsiCo Product Facts (24 fl oz bottle, per 12 fl oz serving)Source