Battleships or heavy cruisers?..you make the call

The did see the Amagiri, but the problem was that the were just idling along - so as to leave no wake - the phosphorescent wake would have given them away well before. Also, the PTs that had radar had already separated. Low speed & low via ability did them in, but there really were not other options.

 

I think that, for as long as depth allowed it, battleships were suited in fighting around a variable shoreline (like Norwegian fjords,) or numerous islands (like Guadalcanal and Central Philippines.) The difficulty of spotting and tracking them, possibly showing up with little warning, makes a battleship fearsome indeed. Compare those settings with, say, the Bismark and Graf Spee in open sea, or Yamamoto's main force at Midway. The Bismark and Graf Spee were not likely to survive long, while Yamamoto's battleships weren't even a factor at Midway.

A cruiser's speed and range, on the other hand, would serve it well during a mid-ocean campaign.