This paper analyzes an infinite horizon dynamic duopoly with stochastic demand in which firms face costs of absorbing and processing information. Our main result is that the structure of dates at which firms choose to absorb information differ starkly between price and quantity competition. Firms synchronize their actions under price competition whereas they plan sequentially and in an alternating manner under quantity competition. The reason is that under quantity competition the planning firm reduces the uncertainty in the residual demand curve of the inattentive firm which renders planning less attractive for that firm. The opposite holds true under price competition.