I found an article from AIRPOWER, July 1976, Vol. 6 No. 4, from Col. "Kit" Carson, in which he talked about the evaluations of the 109 and the 190......
Regarding the 190, he said that the oil cooler system, which was a "number of finned tubes shaped into a ring of tubes a little larger in diameter than the cooling fan" was fitted into the rounded portion of the cowling just aft of the fan.
"I don't think this was a good idea. For example, my principal aiming point was always the forward potion of an enemy ship; the engine, cockpit, wing root section. If you get any hits at all, even only a few, you're bound to put one or two slugs into the engine compartment. Having a couple of bullets riccochet off the engine block and tear up some igniton harness is not bad at all, at least not fatal. But to have all those thin-walled oil cooling tubes ahead of the engine is bad news. Any hits or riccochets in the engine section are bound to puncture the oil tubes. Then the whole engine is immersed in oil spray, and sometimes it would flash over into a fire. All of the 12 FW's I shot down sent off a trail of dense, boiling smoke heavy enough to fog up my gun camera lens and windshield if I were so close."
Not sure how much engine oil the 190 had onboard, but the P47 carried a 28.6 gallon oil tank for the engine. Maybe the 190 had less oil, and ran out of oil faster?