Longitudinal monitoring of BCR-ABL transcript levels in peripheral blood of CML patients treated with tyrosine kinase inhibitors (TKI) revealed a typical biphasic response. Although second generation TKIs like dasatinib proved more efficient in achieving molecular remission compared to first generation TKI imatinib, it is unclear how individual responses differ between the drugs and whether mechanisms of drug action can be deduced from the dynamic data. We use time courses from the DASISION trial to address statistical differences in the dynamic response between first line imatinib vs. dasatinib treatment cohorts and we analyze differences between the cohorts by fitting an established mathematical model of functional CML treatment to individual time courses. On average, dasatinib-treated patients show a steeper initial response, while the long-term response only marginally differed between the treatments. Supplementing each patient time course with a corresponding confidence region, we illustrate the consequences of the uncertainty estimate for the underlying mechanisms of CML remission. Our model suggests that the observed BCR-ABL dynamics may result from different, underlying stem cell dynamics. These results illustrate that the perception and description of CML treatment response as a dynamic process on the level of individual patients is a prerequisite for reliable patient-specific response predictions and treatment optimizations.