Two versions of a vertical product differentiation model, one with fixed and the other with variable costs of quality, are analysed to study how the hypotheses of price versus quantity competition affect equilibrium solutions. Product differentiation arises under all the scenarios considered, contrasting previous findings of symmetric quality choices under Cournot behaviour. However, to relax harsher market competition, firms differentiate more under Bertrand than under Cournot. A simple welfare measure also indicates that the economy is better off when firms compete on prices (with fixed costs of quality, not only consumer but also producer surplus is higher under price competition).