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The Alaska would be a close match.
The German 11" guns had quite light shells 700 lbs but they were accurate, fast firing and had a good size burster charge 41 lbs. The problem was against deck armour the velocity was too high and the angle too shallow to be good against horizontal armour. Not much use v Battleships that can suck up an 11" APC but very handy taking on Cruisers.
The 15" seems to be much better but you have a slower firing gun and a 3 round salvo. Chances of hitting are considerably less maybe half.
With the 11" they were super heavy cruisers and had no business clashing with a Battleship. With 15" they are Battlecruisers and have no business clashing with a Battleship.
Why are they to be considered as Battlecruisers if the guns are 15 in?
The belt is too thick to call it a battlecruiser.
The original Battlecruisers were so called because they had Battleship guns but Heavy Cruiser protection. It's my personal opinion but 11" guns make them a very Heavy well protected Cruiser.
In any form the S&G cannot stand toe to toe with a modern Battleship even a modernised Super Dreadnought would also slap them very hard before they could use their speed to disengage. The only reason Scharnhorst lasted so long against Duke of York was the weather and the fact that Scharnhorst ran like the wind. If it had been a toe to toe slog Scharnhorst would have lasted minutes.
The only time that S&G met an equal was HMS Renown off Norway and they both disengaged with difficulty. Suffering from water entering the main armament and taking several hits from Renowns big hammers. Renown was over 20 years older.
Perhaps I was not clear in the 1st post - intention was the 15 in gunned offspring of S&G are actually made instead of B&T, and consequences of that.
I would say the armour is thicker on Scharnhorst than your giving. The belt is getting on to 14 inches. Although deck armour is on the thin side.
Oh, that was wonderfully awful.If S&G can get through the Panama canal
Tirpitz did very little but had a much bigger effect than Bismarck just by existing.