We consider a duopoly competing in quantity, where firms can invest in both innovative and absorptive R&D to reduce their unit production cost, and where they benefit from free R&D spillovers between them. We analyze the case where firms act non cooperatively and the case where they cooperate by forming a research joint venture. We show that, in both modes of play, there exists a unique symmetric solution. We find that the investment in innovative R&D is always higher than in absorptive R&D. We also find that the value of the learning parameter has almost no impact on innovative R&D, firms profits, consumer's surplus and social welfare. Finally, differences in investment in absorptive research and social welfare under the two regimes are in opposite directions according to the importance of the free spillover.