I'm reading Max Hasting's Inferno and it got me wondering. By military ships I mean ships with guns, like battleships and such.
Let us take a look at the five capital ships lost by the Royal Navy in WWII.
I would actually argue compared to the other contributors that for military ships, guns were a major threat compared to torpedoes.
I make this argument entirely based off the night surface actions in the Guadalcanal campaign, which were fights between fleets primarily consisting of destroyers and cruisers, with the occasional battleship here and there.
It should be noted that in conflicts between the US Navy and the Imperial Japanese Navy, the IJN was widely viewed as having superior torpedoes. The dreaded "Long Lance" torpedo had incredible range, was undetectable (due to using oxygen, which unlike US Mark 14 torpedoes which used carbon dioxide, left a bubble trail that was not visible to an observer, at the cost of being extremely volatile due to carrying extremely flammable gas), and was extremely common among Japanese ships. Typically they were fired in salvos of four from one or two quad torpedo projectors mounted on the side of a ship, although two Japanese light cruisers (Kitakami and Oi) were equipped with 40 torpedo launchers (that perhaps fortunately never saw action). However, torpedoes are extremely hard to aim, have shorter range than even destroyer guns, and more often than not require an enemy to be damaged or unaware to achieve success.
On the other hand, US ships had superior gunnery. Fire-control radar was being introduced, giving US ships highly improved accuracy, even at night. While the Long Lance torpedo could theoretically have a longer effective range than that of a destroyer's 5" gun, a heavy cruiser's 8" gun outranged it significantly, thus giving the US superior first strike capability in a surface action if it so chose (as it was more accurate and longer ranged than the Japanese equivalent, the 20.3cm 3rd Year Gun).
Exhibit 1: Savo Island
At Savo Island, the predominant theme was a night action by a Japanese cruiser force against an unsuspecting US cruiser escort. Most of the US ships were disabled by heavy cruiser gunfire before being finished off by torpedoes. Most US hits on the Japanese ships were by gunfire. Several initial Japanese torpedo volleys missed, and it is thought that at least one US torpedo may have been friendly fire.
Exhibit 2: First Naval Battle of Guadalcanal
Japanese initial salvos from the battlecruisers Hiei and Kirishima decapitate the US fleet's chain of command. In response US surface gunnery takes out a Japanese destroyer, and three US destroyers at close range disable Hiei with cannon fire and machine guns. Cannon fire disables several more US destroyers, and a couple of close-range torpedoes sink one US destroyer and cripple two already damaged cruisers, one mortally. Hiei finally sunk by air attack in the morning.
Exhibit 3: Second Battle of Guadalcanal
US destroyer screen destroyed by Japanese combined gunfire and torpedo attack. Battleship South Dakota takes many gunfire hits, being heavily damaged, or "dumb, deaf, and blind." Battleship Washington leaves Kirishima dead in the water with a quick flurry of shells, then finishes off another Japanese destroyer with another series of gunfire hits. Both South Dakota and Washington evade all torpedoes.
Exhibit 4: Battle at Tassafaronga
US cruiser force intercepts a Japanese destroyer squadron attempting to resupply Guadalcanal. Gunfire quickly sinks a Japanese picket destroyer but torpedoes miss. Japanese destroyers fire a volley of torpedoes unnoticed by the Americans, who are maintaining a tight formation, resulting in numerous torpedo hits that puts a bunch of US heavy cruisers out of the war for months.
The trend in these battles that, unless the ships are inhibited in some way from reacting to torpedoes (i.e. maintaining a formation, caught by surprise, in very close range), that gunfire is almost always more effective at taking out ships. While an individual shell may do less damage than a torpedo hit, the sheer volume of fire, the lack of effective counter measures (like evasion), and the ability to hit areas of importance (like magazines, the bridge, etc.) made gunfire a substantial hazard to ships.
Torpedoes, by far -- there were relatively few ship-to-ship engagements that used big guns in either theater. Most shipping lost (military or non-military) was lost to either aerial attack or to submarines. The loss of the Japanese carriers at Midway is the only major engagement that I can think of (off the top of my head) where bombs did more damage than torpedoes, and the Japanese carriers were uniquely vulnerable to bombs because of their design, damage control doctrine, and the presence of fueled aircraft in their hangar bays. (Even so, the Japanese Kaga and Akagi, and the American Yorktown, were scuttled by torpedoes after they were too damaged to fight on. Another Japanese carrier may also have been scuttled, but I'm going from memory, and not sure.)