Volks have better max range dps than conscripts, but conscripts win up close, so winning engagements depends on your positioning, among other things.
I've had success with conscripts vs OKW using two different commanders.
Here's a nice commander reference guide made by our community.
The first, one I hadn't used in a long time until recently is Guards Rifle Combined Arms Tactics (Guards, Hit the Dirt, PPSH, howitzer, IL2 strafe).
The build is 3x Conscript, t1 for either sniper or m3, 1 or 2 guards, t4 for Su85s and Kats.
As stated, the build revolves around
Combined Arms. Earlygame requires smart use of the 3 conscripts to pick fights where you will win or harass territory if they're bunched up. Conscripts succeed by doubling up vs 1 squad, using buildings, getting up close to volks, cutting off, whatever they can do to stall for the first fight or two.
The engineer caps one point and then builds t1 so you can have a sniper or flamer m3 to support the conscripts. The m3 isnt as timid vs OKW as it is vs Wehr's panzerfausts, so you can push back volk and sturm alike until they upgrade a shreck or get a raketenwerfer, in which case the m3 is maneuverable enough to flank or harass other spots.
You only really need 1 sniper, just enough to pick off charging sturms and spot/harass HMGs so conscripts can flank. Hit the dirt has its uses, and can help stall while the sniper picks off important targets. Then guards come in to help hold ground and solidify your combined arms. This build doesn't really let you spam mines because you have to save up munis for some guards and PPSHs for conscripts.
This grants a pretty good early midgame with this build, though, because empowered conscripts, a sniper, and guards work pretty well together vs OKW. The build is mobile enough to dodge IFGs, capable enough to compete with OKW midgame infantry, and versatile enough to hold off light vehicles. OKW structures have counters in the form of the Katyusha, SU85, and ML-20 (I dare you to put down a forward HQ!).
Vs the terror of OKW lategame the sniper (with vet1 sprint he's hard to kill) and IL2 can help support conscripts and guards vs Obers and blobs. Also, Su85s and guards are still a very potent combo vs heavy vehicles, especially if you can keep an SU85 alive to vet 3 for that insane rate of fire! No flashy tanks, though. Most importantly, the build is fun to use because I sure don't see it too often lately.
As for other conscript-centric builds I enjoy counterattack tactics a lot. On maps like Stalingrad I avoid maxims and try to outmaneuver and harass with conscripts using molotovs until you get shocks, which is where the tide turns. If you haven't tried the KV-1 in a while you should, it's not useless like it was initially. It has awesome armor and a decent gun, so it's good as a frontline tank coordinating with
other armor or AT, not attempting to solo lategame armor. Use it with Su85s, Zis, or flanking t34s because it can survive frontal engagements while other units support it.
Got kinda off-topic but I do think a 3 or 4 conscript start does have a place vs OKW with the right support.