With the Lead Belly perk, you take 50% less radiation every time you drink from an irradiated water source. In Fallout: New Vegas, this benefit extends to all irradiated food and drink.
The usefulness of this perk is debatable, since RadAway and Rad-X become fairly common items later on in both games. In addition, several types of apparel, including some types of power armor, have radiation resistance.
The Rad Resistance perk is a better choice, for it works on water sources and other sources (like foods). For example: taking Lead Belly brings the 5 rads/sec of a fire hydrant to 2 rads/sec but doesn't affect things such as Nuka-Cola. The Rad Resistance perk added to the character's base 10% (assuming 5 Endurance) gives 35% resistance. With 35% resistance, the same fire hydrant is lowered to 3 rads/sec plus Nuka-Cola's 2 rads/sec is lowered to 1 rad/sec and in addition, all environmental radiation sources have reduced effect.
In Fallout: New Vegas, there is an abundance of clean water, reducing the usefulness of the perk, although the benefit is extended to all irradiated food and water.