In this paper, we focus on a packet scheduling algorithm exploiting multiuser diversity in wireless networks. We compare the delay performance of the individual user under the scheduling algorithm exploiting multiuser diversity with that under the round-robin (RR) scheduling algorithm in order to reveal the characteristics of the scheduling algorithm exploiting multiuser diversity. For this purpose, we develop an approximate formula to estimate the tail distribution of packet delay for an arbitrary user under the scheduling algorithm exploiting multiuser diversity and under the RR scheduling algorithm. Numerical results exhibit that, in contrast to the throughput performance of the overall system, the scheduling algorithm exploiting multiuser diversity is not necessarily superior to the RR scheduling algorithm for the delay performance of the individual user. More specifically, it is shown that the former is superior to the latter only when the system lies in a severe environment, e.g., when the arrival rate is large, the burstiness of the arrival process is strong, or the average signal-to-noise ratio is low.