Yeah, but Adams power is a little more advanced than Claires. He doesn't age. We don't know if Claire doesn't age though I guess.
"Adam Monroe seems to have lived for centuries without aging significantly. Angela Petrelli confirms that this is an effect of his ability (Cautionary Tales)"
I don't think Nathan is actually part of the family, he might be adopted. Arthur passed on his power stealing abilities to Peter and Sylar by way of passing his genes to them probably. But Nathans ability is flight, and his power was given to him. Claire probably got her power from given to her by them taking Adams blood and extracting the DNA from it or whatever and implanting it in her.
So it seems the person with the initial power has a more powerful form of the power, and those who get the powers from the initial person (by the powers being given to them, or by way of genetics) is more diluted.