Further, by Stalingrad, the average Russian soldier was more heavily armed then the average German. The days of every third man with a rifle were 1941 and the very beginning of 1942. By mid 1942, Russian industry (which had spent 1941 in transit) was producing something like a million rifles a month. The Germans also prefereed the Russian PPD submachinguns since they were more rugged. The Germans also maintained several battalions of T-34/76s.
I would disagree; I think the Soviets were on the ropes at Stalingrad. Morale was very bad; "deserters and cowards" being shot out of hand. Stalin needed a victory for his troops; something more than the "Not a Step Back" order. The Germans on the Volga were a long way toward accomplishing what they needed to do economically. Everyone thinks they were after the Soviet oil in the Caucasus, which they were, and that they needed it, which they did not. Germany had a sufficient amount in Rumania. The problem was getting it to the front. By blocking Volga barge traffic and north-south rail lines through Stalingrad, the Germans were in a position to DENY the Soviets their own oil. Eventually, they would have strangled the USSR if they could have kept their positions.
That almost happened, too. The Germans slated a number of strong panzer formations to back up the Rumanian armies on the flanks at Stalingrad, but gave priority to feeding the meatgrinder in the City. The operations you refer to by Manstein were done with panzer divisions that got there too late to stop Operation Uranus. If the Germans had pulled back to siege positions around Stalingrad after October 15, and made strengthening the flanks a priority, Uranus would be in the toilet, so to speak. Open tank fighting on the steppe in late 1942; advantage, Germany, by a big margin.