Conventional materials vary their electromagnetic properties in response to the frequency of an incoming wave, but these responses generally remain unchanged at the same frequency unless nonlinearity is involved. Waveform-selective metasurfaces, recently developed by integrating several circuit elements with planar subwavelength periodic structures, allowed us to distinguish different waves even at the same frequency depending on how long the waves continued, namely, on their pulse widths. These materials were thus expected to give us an additional degree of freedom to control electromagnetic waves. However, all the past studies were demonstrated with waves at a normal angle only, although in reality electromagnetic waves scatter from various structures or boundaries and therefore illuminate the metasurfaces at oblique angles. Here we study angular dependences of waveform-selective metasurfaces both numerically and experimentally. We demonstrate that, if designed properly, capacitor-based waveform-selective metasurfaces more effectively absorb short pulses than continuous waves (CWs) for a wide range of the incident angle, while inductor-based metasurfaces absorb CWs more strongly. Our study is expected to be usefully exploited for applying the concept of waveform selectivity to a wide range of existing microwave devices to expand their functionalities or performances in response to pulse width as a new capability.