We study quality competition in a mixed oligopoly (with applications to health care and education) where a welfare-maximising public provider competes with two profit-maximising private providers that differ with respect to the regulatory regime they face, with only one of the private providers being included in the public funding scheme. We find that changes in the funding scheme or in the degree of competition have differential effects on quality provision across the different types of providers and thus generally ambiguous effects on average quality provision. In terms of social welfare, we find that the two policy instruments in the funding scheme - price and copayment - are policy complements (substitutes) for sufficiently low (high) levels of the copayment rate. We also identify a welfare trade-off between the public funding scheme´s generosity (price level) and the extent (number of private providers included).