Purpose: The accuracy of analytical dose calculations (ADC) and dose uncertainties resulting from anatomical changes are both limiting factors in proton therapy. For the latter, rapid plan adaption is necessary; for the former, Monte Carlo (MC) approaches are increasingly recommended. These, however, are inherently slower than analytical approaches, potentially limiting the ability to rapidly adapt plans. Here, we compare the clinical relevance of uncertainties resulting from both. Methods and Materials: Five patients with non-small cell lung cancer with up to 9 computed tomography (CT) scans acquired during treatment and five paranasal (head and neck) patients with 10 simulated anatomical changes (sinus filling) were analyzed. On the initial planning CT scans, treatment plans were optimized and calculated using an ADC and then recalculated with MC. Additionally, all plans were recalculated (non-adapted) and reoptimized (adapted) on each repeated CT using the same ADC as for the initial plan, and the resulting dose distributions were compared. Results: When comparing analytical and MC calculations in the initial treatment plan and averaged over all patients, 94.2% (non-small cell lung cancer) and 98.5% (head and neck) of voxels had differences <±5%, and only minor differences in clinical target volume (CTV) V95 (average <2%) were observed. In contrast, when recalculating nominal plans on the repeat (anatomically changed) CT scans, CTV V95 degraded by up to 34%. Plan adaption, however, restored CTV V95 differences between adapted and nominal plans to <0.5%. Adapted organ-at-risk doses remained the same or improved. Conclusions: Dose degradations caused by anatomic changes are substantially larger than uncertainties introduced by the use of analytical instead of MC dose calculations. Thus, if the use of analytical calculations can enable more rapid and efficient plan adaption than MC approaches, they can and should be used for plan adaption for these patient groups.