The South Dakota design originated from a Chief of Naval Operations request for a new battleship design to be constructed during Fiscal Year '39. Two were originally asked for by the Navy, but Congress on its own authorized another two due to the deteriorating situation around the world.  
       The South Dakota class was a remarkable development over the North Carolinas. That latter design had, in the eyes of most naval officers, serious defects: slow speed, weak protection, and a certain backwardness in technology.  
       The main problem with the desire to build a better battleship was the strict 35,000-ton limit that still applied to any new U.S. battleships at the time of the construction of the South Dakota class. It had been used up completely in the North Carolina design, and how the additional features were to be attained without even the slightest weight increase was a very complicated question.  
        It was a very ingenious solution that the designers found. As a first measure, the same armor belt that North Carolina  had was further inclined to 19°. In addition, the armor belt was transfered from the outside of the hull to  the inside, being replaced on the hull by a 50-pound Special Treatment Steel (usually use for splinter armor) belt which served a decapping function, removing the armor-piercing caps of armor-piercing shells before the actual belt could be reached, a function which equaled another 3.9" of armor. It could decap every shell below 16" and about half the 16" shells.  
        At the same time, a solution to a -- to the U.S. -- previously unknown problem was found: underwater trajectory shells would penetrate battleships so far down on the hull that no armor was available to stop them. The South Dakota design thus attached armor to the lower end of the armor belt that tapered down well into the depth of the ship, decreasing to 1" at its lowest point.  
        This, along with the inherent loss of velocity a shell would have penetrating water, was hoped to be effective protection against underwater trajectory shells.  
       The deficency of this design was the protection against high explosive underwater hits -- i.e. torpedoes and mines -- which prior designs met by using deformating, elastic bulkheads to absorb much of the energy of the explosion. Now, with an unelastic armor belt in this system, it was of doubtful value.  
        On South Dakota  herself, the problem of gaining weight for fleet flagship facilities, which neither ship of the North Carolina class had, was solved by removing two 127mm twin mounts from amidships and adding another level in the armored conning tower.  
        The excellent protection against 16" shells striking both above and under water, however, had to be paid for with two problems: a cramped and short ship requiring higher power for the same speed of 28 knots; and a loss in already rather weak underwater protection. This amounted to the final critique about the South Dakota class -- they were excellent fighting ships, but where sea-keeping and habitability were concerned, the North Carolina class was superior.  
        South Dakota herself stood the test of her armor when she was engaged by the Japanese battleship Kirishima in the Second Naval Battle of Guadalcanal. Her armor was never pierced, neither the belt nor the conning tower, but hits in her unarmored superstructure and an electric fault early in the action severely hampered her fighting ability. Effectively blinded, she only engaged late and failed to make a significant contribution.  
        She was never used in her designed fleet flagship role, and even the force flagship role (flagship to Commander Battleships Pacific Fleet) was executed by Washington carrying Rear-Admiral Willis "Ching" Lee.  
        A comparison between the only two treaty battleship designs made by the  U.S. is probably in order. With so little combat experience for both designs, it  is rather difficult, but the increased armor protection of the South Dakota class would defintely make her a superior fighting ship. At the same time, neither she nor North Carolina could claim perfect handling at sea -- both designs were prone to vibrations at high speeds. The North Carolina design was certainly less cramped, and a better place to live in than the South Dakotas. It must also be attested that however weak the North Carolinas' underwater protection, the South Dakotas' was not better; indeed, as Friedman attests, significantly worse. This could have amounted to special problems considering the proficency displayed by Imperial Japanese forces with the use of torpedoes.  
        Bearing that in mind, in a large-scale fleet engagement such as envisaged before the war, the differences between the two classes might not have made much of a difference (Indeed, at similiar combat ranges, the only two Japanese ships against whose fire South Dakota did, and North Carolina did not, possess a significant immunity zone, were the two battleships of the Nagato class.). On paper, it is likely that South Dakota would have come out the winner, but as stated before, no actual combat test occured under conditions that would make comparison possible.  

Ships in class:  
BB-57 South Dakota  
BB-58 Indiana  
BB-59 Massachusetts  
BB-60 Alabama