The *branching* ratio is 50/50 to about 10e-5 accuracy. This is predicted from the standard model and verified by a *lot* of experimental evidence. You can learn the standard model, and atomic models yourself if you don’t believe it, you don’t even need to go that advanced in the theory in fact. Remember for atomic models (strong force) 150KeV is not really that much hotter than 1KeV. Note we are not talking about the fusion cross section (reaction rate) that’s dominated by tunneling and the electric force, we are talking about the branching ratio “after” a fusion event that’s dominated by the strong force.
There is the DD-He4+2gamma, but this is extremely rare. You must have 2 gammas to conserve all the relevant quantum numbers. So you end up with a fine structure constant squared in the branching ratio and thus you have 50-50 for DD->T+p and DD->He3+n with almost zero contribution from DD->He4.
It may gain some temperature dependence when you get to the 1GeV per nucleon and higher ranges. But probably not. Since the *fusion* branching ratio is still via the same process (you form a He4* intermediate).