In this letter, we consider an intelligent reflecting surface (IRS)-aided wireless communication system, where an active or passive IRS is employed to assist the communication between an access point and a user. First, we consider the downlink/uplink communication separately and optimize the IRS placement for rate maximization with an active or passive IRS. We show that the active IRS should be deployed closer to the receiver with the IRS's decreasing amplification power; while in contrast, the passive IRS should be deployed near either the transmitter or receiver. Moreover, with optimized IRS placement, the passive IRS is shown to outperform its active counterpart when the number of reflecting elements is sufficiently large and/or the active-IRS amplification power is too small. Next, we optimize the IRS placement for both active and passive IRSs to maximize the weighted sum-rate of uplink and downlink communications. We show that in this case, the passive IRS is more likely to achieve superior rate performance. This is because the optimal active-IRS placement needs to balance the rate performance in the uplink and downlink, while deploying the passive IRS near the transmitter or receiver is optimal regardless of the uplink or downlink.