Actually, that happens rarely because the StuG is rather slow and can't really catch up all that easily, not because the StuG has weak DPS or whatnot.
Speed, maneuverability and a turret are part of what make the m10 so deadly. Stug is designed on a different concept for being more durable but in the end I still think the m10 can just create more havoc.
MG42 upgrade + skirts. Now, go get loose on the instantly suppressed infantry - StuG powerslide is just awesome.
Personally I don't think most sane axis person will try to run over American infantry. It's easy to tell if the axis have schreck, while the AT nade is inaccurate and the faust doesn't do much damage. Most Rangers and Airborne are packing ATW and getting stick'd is a death sentence. Maybe it's just a different mind set.
If we sent a vanilla M10 against a vanilla P4 in a slugfest - the P4 would actually win in most cases. It's when we factor in the M10 kiting or having the T3 Armor Plating that the M10 begins to win.
Most people use the m10 to attack target of opportunitys. Attacking an already weaken PZIV or even just plain Kiting. The M10 are great at using such tactic and I think it's understating the m10's lethality if we just gauge its strength using slugfest as a test.