Brain health is most likely compromised after hospitalization for COVID-19; however, long-term prospective investigations with matched control cohorts and face-to-face assessments are lacking. To assess whether long-term cognitive, psychiatric, or neurological complications among patients hospitalized for COVID-19 differ from those among patients hospitalized for other medical conditions of similar severity and from healthy controls. This prospective cohort study with matched controls was conducted at 2 academic hospitals in Copenhagen, Denmark. The case cohort comprised patients with COVID-19 hospitalized between March 1, 2020, and March 31, 2021. Control cohorts consisted of patients hospitalized for pneumonia, myocardial infarction, or non-COVID-19 intensive care-requiring illness between March 1, 2020, and June 30, 2021, and healthy age- and sex-matched individuals. The follow-up period was 18 months; participants were evaluated between November 1, 2021, and February 28, 2023. Hospitalization for COVID-19. The primary outcome was overall cognition, assessed by the Screen for Cognitive Impairment in Psychiatry (SCIP) and the Montreal Cognitive Assessment (MoCA). Secondary outcomes were executive function, anxiety, depressive symptoms, and neurological deficits. The study included 345 participants, including 120 patients with COVID-19 (mean [SD] age, 60.8 [14.4] years; 70 men [58.3%]), 125 hospitalized controls (mean [SD] age, 66.0 [12.0] years; 73 men [58.4%]), and 100 healthy controls (mean [SD] age, 62.9 [15.3] years; 46 men [46.0%]). Patients with COVID-19 had worse cognitive status than healthy controls (estimated mean SCIP score, 59.0 [95% CI, 56.9-61.2] vs 68.8 [95% CI, 66.2-71.5]; estimated mean MoCA score, 26.5 [95% CI, 26.0-27.0] vs 28.2 [95% CI, 27.8-28.6]), but not hospitalized controls (mean SCIP score, 61.6 [95% CI, 59.1-64.1]; mean MoCA score, 27.2 [95% CI, 26.8-27.7]). Patients with COVID-19 also performed worse than healthy controls during all other psychiatric and neurological assessments. However, except for executive dysfunction (Trail Making Test Part B; relative mean difference, 1.15 [95% CI, 1.01-1.31]), the brain health of patients with COVID-19 was not more impaired than among hospitalized control patients. These results remained consistent across various sensitivity analyses. This prospective cohort study suggests that post-COVID-19 brain health was impaired but, overall, no more than the brain health of patients from 3 non-COVID-19 cohorts of comparable disease severity. Long-term associations with brain health might not be specific to COVID-19 but associated with overall illness severity and hospitalization. This information is important for putting understandable concerns about brain health after COVID-19 into perspective.