Optoacoustic imaging is a rapidly developing area of biomedical imaging due its combination of rich optical contrast and ultrasound depth penetration. Just like conventional pulse-echo ultrasound imaging, optoacoustic tomography relies on the use of ultrasound detector arrays with a large number of elements. The precise knowledge of the transducer's sensitivity is crucial for the prediction of its performance for a given imaging task. Sensitivity characteristics such as the central frequency and bandwidth are routinely characterized. However, this characterization is typically performed solely under normal incidence since the measurement of the angle and frequency depended sensitivity (directivity) is difficult and time consuming with existing ultrasound characterization methods. We present a simple and fast characterization method for broadband directivity measurements of the angular transducer sensitivity based on the optoacoustic effect. The method utilizes a thin absorbing suture in order to generate omnidirectional and broadband optoacoustic signals, which are calibrated using a needle hydrophone. We applied this method to characterize and compare the directivity of a conventional piezoelectric (PZT) transducer to the directivity of a capacitive micromachined ultrasonic (cMUT) transducer. Both technologies showed a similar broadband response at normal incidence and the PZT transducer displayed a more than two times larger signal to noise ratio at normal incidence. However, the cMUT transducer's sensitivity was significantly less angle-depended and outperformed the PZT's sensitivity for angles larger than 20°.