Intelligent reflecting surface (IRS) is a new promising technology that is able to reconfigure the wireless propagation channel via smart and passive signal reflection. In this paper, we investigate the capacity region of a two-user communication network with one access point (AP) aided by $M$ IRS elements for enhancing the user-AP channels, where the IRS incurs negligible delay, thus the user-AP channels via the IRS follow the classic discrete memoryless channel model. In particular, we consider two practical IRS deployment strategies that lead to different effective channels between the users and AP, namely, the distributed deployment where the $M$ elements form two IRSs, each deployed in the vicinity of one user, versus the centralized deployment where all the $M$ elements are deployed in the vicinity of the AP. First, we consider the uplink multiple-access channel (MAC) and derive the capacity/achievable rate regions for both deployment strategies under different multiple access schemes. It is shown that the centralized deployment generally outperforms the distributed deployment under symmetric channel setups in terms of achievable user rates. Next, we extend the results to the downlink broadcast channel (BC) by leveraging the celebrated uplink-downlink (or MAC-BC) duality framework, and show that the superior rate performance of centralized over distributed deployment also holds. Numerical results are presented that validate our analysis, and reveal new and useful insights for optimal IRS deployment in wireless networks.