Well, historically it would have surely made the most sense if both types had been used in both armies simultaneously. I don't think it makes no sense that Obersoldaten use MG34 instead, as the MG34 was still used and even produced until the end of the war even though the MG42 was cheaper to produce, which is not really a factor in CoH2 even though that would be its main advantage historically.
From what I remember (you may correct me), from the sources I heard the combat differences between MG42 and 34 are not that big and some soldiers are claimed to even have prefered the MG34 because of small detail differences or maybe they just liked the MG34 more because it probably "felt" more valuable.
But yeah, no use discussing about history I think when both guns should remain balanced in comparison to the Maxim
You are right, both types were used throughout the war, but historical accuracy is not respected: MG42 was cheaper to produce, since it was a simplified design of the MG34 (actually half the build time, and 60% cost) In the game we have a cheaper MG34 => first inaccuracy.
MG42 had also the higher fire rate of the two, with 1200 rpm (upgraded to 1800 by the end of the war), while MG34 was 'only' firing at 800-900 rpm. The MG34 has a better suppression in game=> second inaccuracy.
MG34 production was also halted when MG42 entered mass-production, but it saw use until the end of the war, mostly it's vehicle variant, MG34T.
Accuracy would mean (and yes, i know i am nitpicking here, because it is not relevant to balance) that infantry support HMG of Wehrmacht should be MG34 (since this is the incarnation of the German army of 1940 - 1943), and the infantry version of the Oberkommando weapon should be MG42 (German army from 1943 -1945). Both faction's vehicles should be named MG34 though, as MG42 saw almost no use as a vehicle machine gun.
As for the details, i only know what wikipedia has to offer, i actually do not know what were soldiers of that time frame thoughts about the two versions. Apparently, MG42 (thanks to the simplified design) was more robust and lighter, and would resist to dust a bit more, while being a bit more prone to overheat than the MG34.