One application of gene expression arrays is to derive molecular profiles, i.e., sets of genes, which discriminate well between two classes of samples, for example between tumour types. Users are confronted with a multitude of classification methods of varying complexity that can be applied to this task. To help decide which method to use in a given situation, we compare important characteristics of a range of classification methods, including simple univariate filtering, penalised likelihood methods and the random forest. Classification accuracy is an important characteristic, but the biological interpretability of molecular profiles is also important. This implies both parsimony and stability, in the sense that profiles should not vary much when there are slight changes in the training data. We perform a random resampling study to compare these characteristics between the methods and across a range of profile sizes. We measure stability by adopting the Jaccard index to assess the similarity of resampled molecular profiles. We carry out a case study on five well-established cancer microarray data sets, for two of which we have the benefit of being able to validate the results in an independent data set. The study shows that those methods which produce parsimonious profiles generally result in better prediction accuracy than methods which don't include variable selection. For very small profile sizes, the sparse penalised likelihood methods tend to result in more stable profiles than univariate filtering while maintaining similar predictive performance.