How does caffeine affect urination rate?

Caffeine counteracts ADH, and hence it is a diuretic.

The principle pharmacological effect of caffeine is as an inhibitor of adenosine, meaning it blocks adenosine receptors. Adenosine physiologically constricts the afferent renal artery, meaning it will DECREASE the renal flow rate. This decrease leads to less urine synthesis, stimulating renin release, increasing Angiotensin II, increasing Aldosterone, and thus more ADH. Therefore administering caffeine BLOCKS adenosine receptors, meaning the renal perfusion will be greater, and due to less renin release, less ADH, production of urine will increase.

The soda drinker would have lower ADH and elevated urine output. His urine will be hypotonic to the person who drank water.