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I have to agree with Dave, since Germany would at all times avoid battle, if given the change, so at an speedadvantage of over 11 knots, the German ship could easily avoid the slow USS Penssylvania and get to a save port or so savely, leaving the USN ship behind, without ever fireing a single round from both sides. German Protocol was to avoid battle if given this change. (You realy need something faster to bring Scharnhorst to battle, something with a speed of some 30+ knots at least.)

Even a Bismarck would avoid battle against such a slow opponent, unless it is in a targetted convoy. Against a Bismarck the unmodernized and weakly protected decks of the USN ship would stand no change against plunging shells close to 2000lbs. At least 6 inch of deckarmor would be needed to give a level of protection needed against the plunging German 15" C-34 shells. Secondly the unmodernized USN BB lacks modern firecontroll and certainly radar in 1941, which is essential in longrange gunnery at sea in WW2. Bismarck and Scharnhorst both had the best optical firecontroll ever put on a ship and both had radar fitted, although a crude one. Both German ships had been seriously exercizing gunnerypratcice before becomming active and were considered to be highly accurate in gunnery, compared to the older USN ships before the War.

Still this would mean the unmodernized pre- Pearl Harbor BB's, such as the Pennsylvania class were at a disadvantage concerning armor, especilally their horizontal protection. High velocity shells behave different from free falling AP or SAP bombs, like the one that destroyed USS Arizona, sistership of the Pennsylvania. Steeply ascending heavy shells have much more momentum than a free falling piece or ordonance and have a much greater penetrating power, which cannot be covered enough by a weatherdeck above the main armored deck, if the later is thinner than some 6 inches at least.

Secondly the placement of the main armored deck is important, since the lower it is, the more it can do against shellfire, while at the same time its effect against bombs is more limmited then. Bismarck (and Scharnhorst as well) had a low placement of their main armored deck, almost at waterline level, giving them excelent protetion against plunging gunfire, although it also meant quite a lot of damage would occure above it, as is shown by Bismarck during her last fight. This means, the German ships are desgned to absorb damage more efficiently than ships with higher mounted main armored decks, like most USN and RN BB's. The later were however better suited for missions against aircraft with bombs.

Conclussion remains the same: the pre-Pearl Harbor USN BB is at a serious disadvantage compared to her twenty or so years younger AXIS opponent in almost all aspects, except defenses against aircraft (and their bombs). Should a Scharnhorst choose to fight one, how unlikely this was considering German protocol, the German ship certainly had the capacity to survive the USN shells fired at here, more easlily than desired, since the deep deck provided sufficient cover to the vitals at all expected ranges, wile her smaller shells would most likely not threaten USS Penssylvania either. At long ranges, the much higher speed of Scharnhorst was a great asset, since the long traveltime of shells would mean, she could get manouvred better and be farther away from the targetted spot, originally locked by the USN gunners, while the slower USN ship could not move that fast and far away, making her easier to hit.

Most likely there would have been a draw, ig both would engage eachother, since the Scharnhorst would most likely withdraw after getting damaged, exploiting her higer speed for this. (Unless bad luck for the Germans would have her having enginetroubles, which frequently occured on her.)