With the Lead Belly perk, 50% less radiation is taken every time you drink from an irradiated water source. In Fallout: New Vegas, this benefit extends to all irradiated food and drink.
Because both games rely on the same engine as Oblivion, which used floating point numbers even if the player only saw rounded whole numbers, it is highly likely that a source of water that goes (for example) from "1 Rad" pre-perk to "1 Rad" post-perk is still accurately treated internally i.e. 1 Rad versus .5 Rad.
At high levels this perk may become redundant; RadAway, Rad-X, and apparel with radiation resistance, such as power armor, become more available and readily obtainable.
In Fallout: New Vegas, there is an abundance of clean water, reducing the relative usefulness of the perk, although the benefit is extended to all irradiated food and water.
With the addition of Implant Y-3 in Old World Blues, this perk potentially becomes redundant, though is still available much earlier and for free. This perk also works on food and the implant does not.
“Your digestive tract has adjusted to the weirdness of the Wasteland! Are you sick of stimpaks? Detest chemistry stations and making your own chess, or constantly scavenging for them? Then look for comestibles and water sources throughout the Commonwealth without the usual "distaste"! Take this perk or ones that help you when you use chems (like Chem Resistant or Chemist).”— Fallout 4 Vault Dweller's Survival Guide description
Taking this perk on early may help out a lot as most manufactured food carries a lot of rads, and RadAway is scarce in the beginning. Conversely, this perk has little value for high-level characters because foods provide only a fixed amount of hit points (whereas stimpaks restore a percentage). If you have two ranks of Solar Powered this perk is worth even less. However, in Survival mode, this perk is necessary due to the rads in food and water needed to stay satiated.
Edit
