Both races receive the benefits of a Long Rest in only 4 hours
In the rules quote about the Elf Feature Trance it explicitly states that you gain the same benefits as a human does from 8 hours of sleep. Since Long Rest specifies a minimum of 8 hours the description of Trance in the rules would then mean that by meditating for 4 hours an Elf receives the exact benefits of resting for 8 hours aka a long rest.
While the warforged Living Construct feature is less explicit, its wording is very close to that of the Elf Trance feature and just on the D&D Next rules alone should work the same way.
In 4e Warforged have an identical feature
In 4e what D&D Next calls a Long Rest is called an Extended Rest.
Warforged have the Unsleeping Watcher feature.
Unsleeping Watcher: You do not sleep and instead enter a state of inactivity for 4 hours to gain the benefits of an extended rest. While in this state, you are fully aware of your surroundings and notice approaching enemies and other events as normal.
In 4e only Drow have the Trance Feature
Trance (Drow): Rather than sleep, drow enter a meditative state known as trance. You need to spend 4 hours in this state to gain the same benefits other races gain from taking a 6-hour extended rest. While in a trance, you are fully aware of your surroundings and notice approaching enemies and other events as normal.
