In World War II, why was the ratio of killed to wounded of the Royal Navy twice that of the US Navy?

The U.S. ships were more sturdily built, with water tight compartments, and took longer to sink. So even when they did sink, there was more time for the crew to escape. U.S. ships had better watertight compartments, and did a better job of preventing enemy shells from reaching the storage areas for bombs, torpedoes, ammunition, and other explosives.

One (bad) example for the British was the HMS Hood. It broke apart and sank in three minutes when shells from the Bismarck and Prinz Eugen landed among her ammunition stores. There were only three survivors out of 1417 crew. On the other hand, U.S. ships like the Lexington and Yorktown took hours to sink; most of their crews were rescued and lived, some wounded. There were only about 300 U.S. casualties in the whole Battle of Midway, and likewise about 650 in the Battle of the Coral Sea, despite the loss of a carrier in each battle. The Yorktown had 141 fatalities, one tenth of the total on the Hood.

Since we are talking of two different sources, we do not know whether their interpretation is the same, specially regarding to wounded men. Light wounds might not be counted in the Royal Navy in the same way that US Navy. Another potential explanation is that UK had more deaths in the beginning of the war, while US had them later, when medical attention was better.

If we check total data from all service branchs we might see the following from wikipedia:

UK deaths: 383,700
UK wounded: 376,239
US deaths: 407,300
US wounded: 671,801

As we can see, the ratio is different for both countries, hence we can't say that the difference was only in the naval branches, US had always more wounded. Hence the ships are not related to the statistics.

One has to consider the situation the two navies were in.

The Royal Navy operated heavily in the north Atlantic on convoy duty and in conflict with German naval forces, and took a lot of casualties, from loss of warships to the RN gun crews on merchant ships. That area is extremely cold; a person thrown into the water without benefit of a survival suit or lifeboat will die of hypothermia very quickly, 10 minutes to a few hours, depending on the temperature. This was especially true of the Murmansk convoys, which skirted the Arctic Circle. Going into the water without a lifeboat or raft there was pretty much a death sentence.

The US Navy took the bulk of its casualties in the central Pacific, a tropical climate, where the temperature is considerably higher. Survivors of a sinking could last for days, when they would start dying from lack of fresh water... a much longer window of opportunity for rescue. They did face one peril not found in the north Atlantic: shark attack. It is estimated that sharks may have killed up to 500 survivors of the USS Indianapolis sinking, so those waters weren't entirely safe.

The combat situation also was quite different.

In convoy duty, the convoy would not stop for a ship sinking - they'd make easy targets for submarines. There was a single rescue ship at the back of the convoy that did pick up what survivors it could find, usually a small ship not meriting a torpedo. In the case of the Hood, the only other British ship was the Prince of Wales, and it was beating a retreat as it had been damaged and was now alone. It is likely that more than three sailors survived the Hood's magazine explosion, but a combination of cold water and no one to rescue them immediately did in the rest. The crew of the Bismarck met a similar fate - after it's sinking, a report of a U Boat periscope caused the British ships to break off rescue efforts, and consequently a lot of the Bismarck crew that survived the sinking perished.

In the Pacific, much of the action was by air attack. Once the attacking planes had left, the remaining ships had ample opportunity to conduct rescue operations without interference from an opposing force.

Even in the ship on ship actions, such as the fierce conflicts around Guadalcanal, the fleets broke off contact quickly, with the Japanese ships clearing out before daylight would bring dive bombers. This gave time and opportunity to conduct rescue operations without interference.

So the weather and combat situation was quite different where the two navies conducted the bulk of their operations. The Royal Navy operated in a situation that would cause more deaths, from both weather and combat conditions.