Notable cross-country differences exist in the diffusion of the Covid-19 and in its lethality. Contact patterns in populations, and in particular intergenerational contacts, have been argued to be responsible for the most vulnerable, the elderly, getting infected more often and thus driving up mortality in some context, like in the southern European one. This paper asks a simple question: is it between whom contacts occur that matters or is it simply how many contacts people have? Due to the high number of confounding factors, it is extremely difficult to empirically assess the impact of single network features separately. This is why we rely on a simulation exercise in which we counterfactually manipulate single aspects of countries' age distribution and network structures. We disentangle the contributions of the kind and of the number of contacts while holding constant the age structure. More precisely, we isolate the respective effects of inter-age contact patterns, degree distribution and clustering on the virus propagation across age groups. We use survey data on face-to-face contacts for Great Britain, Italy, and Germany, to reconstruct networks that mirror empirical contact patterns in these three countries. It turns out that the number of social contacts (degree distribution) largely accounts for the higher infection rates of the elderly in the Italian context, while differences in inter-age contacts patterns are only responsible for minor differences. This suggests that policies specifically targeting inter-age contacts would be little effective.