That depends on the exact height and length of the barrier as well as the energy of the incident particles. For a given height and length of the barrier you can find an energy less than the height of the barrier for which either particle would have a transmission probability of 1 and the other particle would have something less than 1.
You can see a decent treatment of the problem on Wikipedia. Take a look at the form of the transmission coefficient T for the case [itex]E<V_0[/itex]. If you choose [itex]k_1[/itex] such that [itex]\sin(k_1 a) = 0[/itex] then the transmission coefficient will be 1. [itex]k_1[/itex] depends on the mass of the particle and the difference between the height of the barrier and the energy of the particle.