A fascinating discussion!
The ships were almost a decade apart, but as the crew has pointed out, the loss of the treaty restrictions and the move past the 10,000T=cruiser concept probably opened many design doors that couldn’t be exploited by the German shipbuilders who had to stick closer to that political but not helpful weight limit at a time when so many facilities were being added to ships (radar, sonar, AAA, ASW gear, seaplanes, wartime crew sizes)
Its difficult to see how these kinds of things would work out in practice, as only a single battle (kommandorski isles) was ever fought under the proposed hypothetical circumstances of “all-guns no air support”.
In my study I have found that (in regards to WW2 surface/submarine naval action not counting carrier aviation) while the Americans often had some technical or material advantage in most qualitative regards, that their performance was generally lower than would be expected because of inexperience, poor communication or tactics, unreliable equipment, or surprise. The Germans often performed better than expected at sea, despite having a deficiency of numbers and equipment, and tactics, and the Italians much worse than would be expected given the size and expenditure on their navy.
As with tanks, the Americans did not have spectacular ships, guns, crews, torpedoes, but rather the benefit of having well-designed, average and reliable equipment in adequate quantity and available in abundance at critical times and places. The opposite is true of the Axis; while their systems were stronger in design and performance, (and their preparations for night fighting and innovations of oxygen powered torpedoes, guided missiles/torpedoes etc.) they suffered from over complexity, poor general strategy (fleet submarines, solo raiding by unsupported warships even after PoW/Repulse were easily sunk), weak logistical support and coordination, and substituting novel design and variety for numbers.
So, its a great question as posed, without a date or any help, it may have been a closer match than stated above; the American ship is clearly a more robust, general design, a bigger, newer ship (and probably with a much better radar), even with those advantages, many US/UK ships with similar advantages were utterly mauled, and not just by submarines, mines, guided bombs, human torpedoes, air attacks, but also in face-to-face battles against similar ships. This has a lot to do with the specific situations (savo island, the bismark chase) but not really luck, more Axis moxy.
Couple of lucky hits, and the “better ship” can have an ammo explosion or lose its steam. And under the scenario of no-air no-helpers, 1v1, some luck or moxy might win the day, given the disparity in the attributes of each ship.
Have a great weekend!