Most mobile network operators generate revenues by directly charging users for data plan subscriptions. Some operators now also offer users data rewards to incentivize them to watch mobile ads, which enables the operators to collect payments from advertisers and create new revenue streams.In this work, we analyze and compare two data rewarding schemes: a Subscription-Aware Rewarding (SAR) scheme and a Subscription-Unaware Rewarding (SUR) scheme. Under the SAR scheme, only the subscribers of the operators' data plans are eligible for the rewards; under the SUR scheme, all users are eligible for the rewards (e.g., the users who do not subscribe to the data plans can still get SIM cards and receive data rewards by watching ads). We model the interactions among an operator, users, and advertisers by a two-stage Stackelberg game, and characterize their equilibrium strategies under both the SAR and SUR schemes. We show that the SAR scheme can lead to more subscriptions and a higher operator revenue from the data market, while the SUR scheme can lead to better ad viewership and a higher operator revenue from the ad market. We further show that the operator's optimal choice between the two schemes is sensitive to the users' data consumption utility function and the operator's network capacity. We provide some counter-intuitive insights. For example, when each user has a logarithmic utility function, the operator should apply the SUR scheme (i.e., reward both subscribers and non-subscribers) if and only if it has a small network capacity.