We can logically choose a best battleship design for some displacement or for some price but to make a sensible choice it would be very helpful to know when and where the ship will operate and what threats it will face.
If we search the internet for best battleships, the most popular choices are the South Dakota and related Iowa designs while Bismarck and Tirpitz have a dedicated following. However, let us imagine that history had taken a few different twists.
Off Guadalcanal South Dakota received a number of hits from Kirishima, Atago and Takao. Most of the shells from Kirishima were nose fused HE or anti-aircraft shells because Kirishima had loaded her guns to bombard Henderson Field rather than to fight a surface action. Only Hit 26 may have been a 14 inch Type 91 AP fired late in the action. However, what if Hit 25 had been a 14 inch AP shell?
http://www.researcheratlarge.com/Ships/ ... html#Hit25 has “An estimated 8-inch AP projectile hit the shell at the second deck, frame 109-1/2. The projectile pierced the shell at a seam between a 25-pound and a 50-pound STS strake, furrowed through the 20-pound STS, second deck, pierced 10-pound longitudinal torpedo bulkhead No. 2 and penetrated the 12.2-inch longitudinal armor bulkhead to a depth of 7 to 8 inches at the top edge of the armor.”
If a 14 inch shell had hit at the same place, it might have retained its cap until it hit the 12.2-inch armor (unlike the actual 8 inch shell). It still might have been stopped by the main deck behind but the shell could have deflected down a little and penetrated.
The South Dakota design aimed at the shortest possible citadel and one of the features was that the secondary magazines were above the machinery. A fire amongst the 6,000 5 inch shells (assuming full magazines) would have been very unpleasant, especially as the magazines were above the waterline and thus relatively hard to flood.
Now assume a much bigger divergence. Let us keep the Anglo-Japanese Alliance (don't ask how) and have Nagato in place of either Rodney on 27th May 1941 or, ignoring the problems of speed, Hood on 24th May. A lucky first hit from Nagato could have penetrated Bismarck's magazine and greatly changed Bismarck's reputation.
In detail, at 20,000 metres range, a shell from Nagato's 41 cm guns would fall with 495 mps velocity and at an angle of 17.5 degrees according to
http://www.navweaps.com/Weapons/WNJAP_161-45_3ns.htm. To hit 3.5 metres below the waterline at 17.5 degrees angle of fall, implies that shell struck the water 11.1 metres short of the ship and travelled 11.64 metres through the water. 11.64 metres is 28.4 times 41 cm. The rough estimate was that a Type 91 shell lost half its velocity over 100 calibres. Thus we can be fairly confident that the shell would have at least 300 mps velocity on hitting Bismarck's hull and that the total time since hitting the water and initiating the fuse would be shorter than 0.035 seconds. A German or American shell might explode at that point and a British shell would perhaps have already exploded (as a British actually exploded close to the 45 mm bulkhead, we are obviously either making the shell go unnecessarily deep below an undamaged Bismarck's 2.2 metres of armour or underestimating the velocity). A Japanese Type 91 shell had a delay of 0.4 seconds. It would continue until stopped and it might easily stop after deflecting off one of Bismarck's own shells.
The take home message is that WW2 battleships could easily not be designed to survive all plausible threats.
