This isn't in 4 or New Vegas, but when you level up, you gain skill points, which you use to increase your level in certain skills
Leveling medicine increases the health you heal with Stimpacks and the rads you remove with Radaway
Leveling explosives lets you do more damage with explosives, and craft better explosives
There's a whole lot of skills to level up
And certain dialogue choices require you to have a certain level in that skill