Photodiodes are important components in optical data links, and their performance degradation under irradiation has to be understood in order to guarantee the long-term functionality of the data links in radiation environments of high-energy physics experiments. Indium gallium arsenide (InGaAs) on indium phosphide (InP) photodiodes are attractive candidates for these applications, thanks to their relatively modest radiation-induced responsivity loss when operated at 850 nm. In this paper, we present the results that confirm earlier observed additional sensitivity penalties in InGaAs-based receivers. This behavior is further investigated by carrying out several proton tests where InGaAs photodiodes are irradiated together with alternative photodiode types. The critical parameters—responsivity, dark current, and capacitance—are measured up to fluences exceeding ${1\times 10^{16}}$ p/cm². Radiation-induced dark current is shown to be orders of magnitude higher in InGaAs photodiodes than in GaAs and InGaAs on GaAs photodiodes. However, instead of the dark current increase, the additional losses with InGaAs photodiodes are shown to arise from strongly increased capacitance, which is a dominant feature only in InGaAs photodiodes. This is confirmed with simulations where the measured capacitance characteristics are used in the device model. Our results show that without precautions in the receiver design, radiation-induced capacitance can limit the use of InGaAs photodiodes in harsh radiation environments.