I chose the assault rifle. But this is a question which could be argued either way.
My rationale for the assault rifle was that in late '41 the Germans surprised the Soviets by making one last push for Moscow. Has that push succeeded, Moscow would have fallen, and the Soviet war effort would have been altered. The offensive was stopped by Soviets hastily recruited away from their factory positions and put into defensive positions near Moscow. With assault rifles, maybe the Germans would have been able to break those defenses. Not to mention achieving more favorable exchanges in combats prior to the battle of Moscow.
Over the short run Germany’s biggest problem seemed to be its lack of industrial capacity. During 1942 the Soviet Union out produced Germany by a factor of 3 or 4 in nearly every major weapons category. By 1944 Germany’s military production was triple what it had been in 1942. However, most of the strength of its army had been spent. The assault rifle would have allowed Germany to better preserve that strength, by giving German infantry an important advantage in firefights against their Soviet counterparts.
However, the Soviets also increased their military production from 1942 - '44. Just as they were starting to come toward the end of their truly massive reserves of manpower, they were able to compensate by putting unheard-of numbers of tanks and artillery onto the battlefield.
The assault rifle was needed to deal with the Soviets’ overwhelming numerical advantage, and the Panzerfaust was needed to address the fact that the Soviets were able to produce significantly more tanks than the Germans. (Not to mention all the tanks they received through Lend Lease.) Soviet tanks were also superior to the Germans’, at least until the latter began building large numbers of Panthers and Tigers.