Postoperative delirium (PD) after transcatheter aortic valve implantation (TAVI) remains to be explored. We sought to (1) determine the incidence of PD in octogenarians who underwent TAVI or surgical aortic valve replacement (SAVR), (2) identify its risk factors, and (3) describe possible differences in the onset and course of PD between treatment groups. A prospective cohort study of consecutive patients aged ≥80 years with severe aortic stenosis who underwent elective TAVI or SAVR (N = 143) was conducted. The incidence of PD was assessed for 5 days using the Confusion Assessment Method (CAM). Risk factors for PD were studied with logistic regression. Patients treated with TAVI were older (p ≤0.001), had lower cognitive scores (p = 0.007), and more co-morbidities (p = 0.003). Despite this, significantly fewer (p = 0.013) patients treated with TAVI (44%) experienced PD compared to patients treated with SAVR (66%). Undergoing SAVR (p = 0.02) and having lower cognitive function (p = 0.03) emerged as risk factors for PD, whereas gender, activities of daily living, frailty, atrial fibrillation, and postoperative use of opioids and anxiolytics did not. Patients treated with TAVI and without PD during the first 2 postoperative days were unlikely to experience PD on subsequent days. The onset of PD after SAVR could occur at any time during the postoperative evaluation. In conclusion, SAVR in octogenarian patients with aortic stenosis might be considered as a predisposing factor for PD. Our data also suggest that the onset of PD was more unpredictable after SAVR.