I am quite sure that soft steel (iron) cores would be outlawed in Germany, if their penetration capability were notably better compared to lead cores. The presence in WW2 German bullets is definitely due to the scarcity of lead, as archive records show. The late war SmE lang (even less lead) could definitely not penetrate a ~4 mm steel plate that was easily penetrated by ordinary lead core S and sS bullets of several lots. Actually that was a French test. The target plate is now in the collection of Wehrtechnische Studiensammlung at Koblenz.
I will ask someone who is experienced in penetration testing regarding the relation of soft steel core versus lead core.
Edit: Just to show the non-trivial matter of penetration. In the NATO trials at Meppen that led to the adoption of SS109, it turned out that at 100 m, the U.S. lead core M193 could penetrate a steel plate which the SS109 with its soft steel penetrator could not. (I will look up the plate thickness.)
The French at Bourges thought the Germans had had a few stiff drinks too much (Lower Saxony is more known for schnaps than for beer) and repeated the test. The result was the same: lead core M193 could penetrate a plate at 100 m which SS109 could not.
Added data: The plate was 7 mm RHA at 100 m with 90 degree impact: M193 penetrated, SS109 did not. RHA is rolled homogenous armor, not mild steel.