Background: A key idea of feature orientation is to decompose a software product line along the features it provides. Feature decomposition is orthogonal to object-oriented decomposition it crosscuts the underlying package and class structure. It has been argued often that feature decomposition improves system structure (reduced coupling, increased cohesion). However, recent empirical findings suggest that this is not necessarily the case, which is the motivation for our empirical investigation. Aim: In fact, there is little empirical evidence on how the alternative decompositions of feature orientation and object orientation compare to each other in terms of their association with observable properties of system structure (coupling, cohesion). This motivated us to empirically investigate and compare the properties of three decompositions (object-oriented, feature-oriented, and their intersection) of 28 feature-oriented software product lines. Method: In an exploratory, observational study, we quantify internal attributes, such as import coupling and cohesion, to describe and analyze the different decompositions of a feature-oriented product line in a systematic, reproducible, and comparable manner. For this purpose, we use three established software measures (CBU, IUD, EUD) as well as standard distribution statistics (e.g., Gini coefficient). Results: First, feature decomposition is associated with higher levels of structural coupling in a product line than a decomposition into classes. Second, although coupling is concentrated in feature decompositions, there are not necessarily hot-spot features. Third, the cohesion of feature modules is not necessarily higher than class cohesion, whereas feature modules serve more dependencies internally than classes. Fourth, coupling and cohesion measurement show potential for sampling optimization in complex static and dynamic product-line analyses (product-line type checking, feature-interaction detection). Conclusions: Our empirical study raises critical questions about alleged advantages of feature decomposition. At the same time, we demonstrate how the measurement of structural attributes can facilitate static and dynamic analyses of software product lines. (authors' abstract)