Ranking the greatest battleships of all time is a tad easier than ranking naval battles. Both involve comparing apples with oranges. But at least taking the measure of individual men-of-war involves comparing one apple with one orange. That's a compact endeavor relative to sorting through history to discern how seesaw interactions shaped the destinies of peoples and civilizations.
Still, we need some standard for distinguishing between battlewagons. What makes a ship great? It makes sense, first of all, to exclude any ship before the reign of Henry VIII. There was no line-of-battle ship in the modern sense before England's "great sea-king" founded the sail-driven Royal Navy in the 16th century. Galley warfare was quite a different affair from lining up capital ships and pounding away with naval gunnery.
One inescapable chore is to compare ships' technical characteristics. A recent piece over at War Is Boring revisits an old debate among battleship and World War II enthusiasts. Namely, who would've prevailed in a tilt between a U.S. Navy Iowa-class dreadnought and the Imperial Japanese Navy's Yamato? Author Michael Peck restates the common wisdom from when I served in mighty Wisconsin, last of the battleships: it depends on who landed the first blow. Iowas commanded edges in speed and fire control, while Yamato and her sister Musashi outranged us and boasted heavier weight of shot. We would've made out fine had we closed the range before the enemy scored a lucky hit from afar. If not, things may have turned ugly.
Though not in so many words, Peck walks through the basic design features that help qualify a battleship for history's elite -- namely guns, armor, and speed. Makes sense, doesn't it? Offensive punch, defensive resiliency, and speed remain the hallmarks of any surface combatant even in this missile age. Note, however, that asymmetries among combat vessels result in large part from the tradeoffs naval architects must make among desirable attributes.
Only sci-fi lets shipwrights escape such choices. A Death Star of the sea would sport irresistible weaponry, impenetrable armor, and engines able to drive the vessel at breakneck speed. But again, you can't have everything in the real world. Weight is a huge challenge. A battleship loaded down with the biggest guns and thickest armor would waddle from place to place. It would make itself an easy target for nimbler opponents or let them run away. On the other hand, assigning guns and speed top priority works against rugged sides. A ship that's fleet of foot but lightly armored exposes its innards and crew to enemy gunfire. And so forth. Different navies have different philosophies about tradeoffs. Hence the mismatches between Yamato and Iowa along certain parameters. Thus has it always been when fighting ships square off.