Users of hearing aids (HAs) and cochlear implants (CIs) experience significant difficulty understanding a target speaker in multi-talker environments or when other background noise is present. Segregation of a particular voice from background noise occurs partly through enhanced cortical tracking of amplitude fluctuations in the target signal. Measuring a person’s cortical tracking allows decoding their focus of attention and may be used for neurofeedback in hearing devices, potentially aiding their users with speech-in-noise comprehension. Most studies on cortical speech tracking have employed typical hearing (TH) individuals, whereas studies in people with hearing impairment whose cortical tracking may differ are still scarce. The objective of this study was to compare cortical speech tracking of HA (n=29) and CI users (n=24) to that of age-matched TH individuals (n=29). We recorded EEG data while the participants attended one of two competing talkers (one with a female and one with a male voice), in a free-field acoustic environment. Importantly, HA users as well as CI users used their personal, clinically-fitted devices. Cortical speech tracking was assessed through linear backward and forward models that related the EEG data to the speech envelope. For the CI users, electrical artifacts stemming from the implant were addressed through a bespoke method for artifact rejection. We found that the HA group exhibited cortical tracking and attentional modulation that were largely comparable to those of the TH group. CI users also showed successful cortical tracking. However, they displayed a profound deficit in attentional modulation, seen in the significantly poorer neural segregation of the attended vs. the ignored speech streams. These results shed light on a neurobiological mechanism for speech-in-noise comprehension and have implications for neurofeedback in hearing devices.