The problem with proton-proton fusion is that there is no bound state of two protons. For the fusion to occur one of the protons has to turn into a neutron by beta plus decay. This is mediated by the weak force so it's a slow process and the probability of it happening while the protons are close enough to form a deuteron is very low. By contrast a deuteron and tritium nucleus readily form $^5$He.
The proton proton fusion cross section isn't known from experiment so only calculated values are known and these are somewhat uncertain. I found this paperthis paper that summarises the reaction rates. The p-p fusion is about $10^{26}$ times slower than the D-T fusion.