Recently the workhorse model of intra-industry trade has been augmented with heterogeneous cost structures at the firm level. In principle there exist various sources of heterogeneity, yet the literature appears -- for convenience or other reasons -- to settle on marginal cost heterogeneity as the preferred modelling device. The present paper develops a unified model framework allowing a systematic comparison of marginal and fixed cost heterogeneity. We find that both types of heterogeneity are in fact able to capture the central stylized facts of international trade. For example can either source of heterogeneity generate the observed higher productivity among export-active firms, the fairly small fraction of firms in a given industry that actually exports, and the larger size of export-active firms. Accordingly, the underlying nature of firms heterogeneity can not be discerned from the ability of competing assumptions to capture the empirical facts. The paper concludes by identifying new allies for empirical research into firm-heterogeneity.