Comparing business process variants using event logs is a common use case in\nprocess mining. Existing techniques for process variant analysis detect\nstatistically-significant differences between variants at the level of\nindividual entities (such as process activities) and their relationships (e.g.\ndirectly-follows relations between activities). This may lead to a\nproliferation of differences due to the low level of granularity in which such\ndifferences are captured. This paper presents a novel approach to detect\nstatistically-significant differences between variants at the level of entire\nprocess traces (i.e. sequences of directly-follows relations). The cornerstone\nof this approach is a technique to learn a directly follows graph called mutual\nfingerprint from the event logs of the two variants. A mutual fingerprint is a\nlossless encoding of a set of traces and their duration using discrete wavelet\ntransformation. This structure facilitates the understanding of statistical\ndifferences along the control-flow and performance dimensions. The approach has\nbeen evaluated using real-life event logs against two baselines. The results\nshow that at a trace level, the baselines cannot always reveal the differences\ndiscovered by our approach, or can detect spurious differences.\n