This paper investigates the R&D (research and development) risk choices of private and public firms in a product differentiated mixed duopoly market. Using the canonical models of R&D risk choice in a mixed market, it compares market performances between Cournot and Bertrand. The main findings are (i) public firm always engages in higher R&D risks than private firm under Cournot, (ii) public firm mostly chooses higher R&D risks, but may choose lower R&D risks than private firm if the degree of product substitution is sufficiently large under Bertrand, (iii) both public and private firms are more willing to take R&D risks under Bertrand than under Cournot, and (iv) from the perspective of social welfare, private firm always assumes too low R&D risks under Cournot. However, it takes excessive risks if the degree of product substitution is large enough under Bertrand.