Now consider two things. Firstly, obviously, which of these is the best combat ship one on one and why? You can assess this by what ships are available in 1941 and in a hypothetical 1946 when all are completed.
Secondly, what design represents the best value for money? Let’s not into whether battleships in general represent good value for money, no one cares about that since this is a theoretical exercise.
Combat ships:
in 1941 - KGV - excellent armour, fast, good AA (for the time), good fire control, adequate guns and good number of them. I think the results speak for themselves there.
Hypothetical 1946 - Iowa - Would cope with anything else on the list (although I suspect it would be close vs Yamato or Vanguard - for different reasons).
High speed, adequate armour, good guns & fire control, good AA.
Good value for money - much trickier.
I'd go for North Carolina - ready in time (well, in time for the Americans anyway
The large hull makes them more practical for long-term use and upgrade. In an alternate 1960, where battleships are still relevant, I can see the South Dakotas being the "USN's R-class" - good ships when built, but built down to a price (or rather treaty), and therefore not capable of being modified as extensively.
Why not Iowa or KGV instead of NC?
Iowa - much more expensive, but relatively not that much better, costlier to run.
KGV - short range, and not individually a Yamato, Iowa or H-class killer; several systems would need costly upgrades in the long term (e.g. AC electrics, dual purpose AA, very high-pressure machinery).