Volks on their own, without Vet, are pretty shoddy. Their DPS is fairly appalling and in a vacuum, a conscript will indeed beat a volksgren hands down, even if the Conscript has to charge.
However, this is negated by the fact the OKW also get Sturmpios early game, which can easily take 2:1 conscript squads if placed in cover properly. The OKW also get access to extremely effective doctrinal infantry, such as Falschirms, the infamous MG34 and Fusiliers/Sturmofficer. Don't even get me started on how quickly Obers chew up conscripts.
Anyway, even with vanilla Volks against vanilla Cons in a 1v1 situation, once you upgrade to your first tech truck and get access to grenades, the balance quickly favors Volks (Simply because of how effective those grenades are). If you go Spec-Ops/Scavenge, you also get access to the assault-gren style grenade volley, which is insanely cost effective for what it does (10 munitions for a potential squadwipe if your opponent is inattentive).
Edit: Volks are worse than Conscripts in an equal engagement. The only way you can trump conscripts with vanilla volks is by blobbing up (Which a Soviet player can do himself).
+1 Great post