Hi XeLa,
My first interrogation is whether there is enough oxygen to burn both gases when they are ignited.
If not, you'll get soot under usual conditions. How much of each gas reacts would be extremely difficult to tell. You might suppose that acetylene is more reactive, but this won't bring clear consequences.
I insist on "when they are ignited". If the oxygen is introduced slowly and the mix is immediately ignited, you get soot, which does not burn afterwards, even if hot and with oxygen.
If the oxygen suffices to burn both gases towards CO and H2O, then you get a complex mix of H2, CO, CO2, H2O, O2 and many more. It even needs more oxygen than this minimum, because the flame in oxygen is much hotter than in air, and the reactions are very incomplete. The temperature keeps a significant amount of H2 and CO together with O2. In air, the big amount of N2 dilutes the heat, the flame is less hot, and the reactions proceed completely to CO2 and H2O if the amount of O2 suffices.
With enough oxygen and a hot flame, the detailed composition of the fuel is unimportant. The temperature suffices to destroy completely the fuel molecules, so the composition of the oxidized products depends just on how much the fuel mix brings of C, H and heat of formation.