The extensive availability of spectrum resources and the remarkably high data transmission rate of millimeter-wave (mmWave) technology have propelled its significance as a vital component in the advancement of mobile communications, including fifth generation (5G) networks. However, the intermittent nature of mmWave links and their interaction with transport layer protocols pose several challenges, which bring inadequate performance, due to fluctuations in high-frequency channels. Consequently, although these features of mmWave might be advantageous, they can actually hinder the performance. Although these issues have been studied in the literature with TCP, there are few works that have studied how QUIC behaves over this kind of channels. This paper aims to compare the performance of TCP and QUIC over mmWave channels, studying the impact at the application level. We conduct extensive performance evaluations, based on traces that are obtained by means of a detailed simulation of different mmWave scenarios, using the ns-3 simulator. We analyze key performance indicators, such as delay, throughput, and bottleneck buffer. The results evince that QUIC outperforms TCP in highly fluctuating mmWave channels, showing better performance for both throughput and delay.