Flexible and intelligent antenna designs, such as pinching antenna systems and reconfigurable intelligent surfaces (RIS), have gained extensive research attention due to their potential to enhance the wireless channels. This letter, for the first time, presents a comparative study between the emerging pinching antenna systems and RIS in millimeter wave (mmWave) bands. Our results reveal that RIS requires an extremely large number of elements (in the order of $10^4$) to outperform pinching antenna systems in terms of spectral efficiency, which severely impact the energy efficiency performance of RIS. Moreover, pinching antenna systems demonstrate greater robustness against hardware impairments and severe path loss typically encountered in high-frequency mmWave bands.