Frequency characteristics of ultrasound detectors used in optoacoustic tomography have a major impact on imaging performance. It is common practice to select transducers based on their sensitivity at the central frequency and under normal incidence. However, the bandwidth and angular sensitivity play an equally important role in establishing the quality and accuracy of the reconstructed images. Here, we developed a calibrated optoacoustic characterization method specifically tailored for broadband measurements of the angular transducer sensitivity (directivity). Ultrawideband omnidirectional optoacoustic responses were generated by uniformly illuminating thin absorbing sutures with nanosecond laser pulses and characterized with a needle hydrophone. This calibrated optoacoustic source was used to characterize the frequency dependence of the angular response by a conventional piezoelectric transducer (PZT) and a capacitive micromachined ultrasonic transducer (cMUT) with similar size and central frequency. Furthermore, both transducers had no preamplification electronics directly attached to the detection elements. While the PZT presented a 7.8 dB sensitivity advantage at normal incidence, it was able to provide detectable signal-to-noise levels only at incidence angles of up to 20 deg whereas the cMUT maintained reasonable sensitivity levels and broadband response at incidence angles of 40 deg and beyond. We further experimentally showcase a reduction in the limited-view image artifacts resulting from the broader acceptance angle of the cMUT.