Multi-modal music classification creates supervised models trained on features from different sources (modalities): the audio signal, the score, lyrics, album covers, expert tags, etc. A concept of "multi-group feature importance" not only helps to measure the individual relevance of features of a feature type under investigation (such as the instruments present in a piece), but also serves to quantify the potential for further improving classification by adding features from other feature types or extracted from different kinds of sources, based on a multi-objective analysis of feature sets after evolutionary feature selection. In this study, we investigate the stability of feature group importance when different classification methods and different measures of classification quality are applied. Since musical scores are particularly helpful in deriving semantically meaningful, robust genre characteristics, we focus on the feature groups analyzed by the jSymbolic feature extraction software, which describe properties associated with instrumentation, basic pitch statistics, melody, chords, tempo, and other rhythmic aspects. These symbolic features are analyzed in the context of musical information drawn from five other modalities, and experiments are conducted involving two datasets, one small and one large. The results show that, although some feature groups can remain similarly important compared to others, differences can also be evident in various applications, and can depend on the particular classifier and evaluation measure being used. Insights drawn from this type of analysis can potentially be helpful in effectively matching specific features or feature groups to particular classifiers and evaluation measures in future feature-based MIR research.