Is a nuclear family more democratic and egalitarian than the extended family?
We cannot say with certainty that every nuclear family is more egalitarian than every extended family. You can certainly have nuclear families with very patriarchal fathers. You can certainly have extended families in which all members are treated equally.
You can argue that a nuclear family is more egailitarian than an extended one because it has fewer generational layers. You can argue that a nuclear family will tend to be more egalitarian because it has fewer members. A married couple with their children can be more egalitarian because their family is smaller and less complicated and can be run more along consensual lines. You can argue that an extended family is so big and potentially confused that it must be run in a less egalitarian way.
However, this is not a hard and fast rule. There can be different levels of democracy and egalitarianism within different families of the same type.