In the Assembly, the opposite is true. There are more Democrats, so that Democrats control the majority of votes taken there and the majority of appointments on each committee. The Speaker of the Assembly is Sheldon Silver. All legislators have one vote, so in that respect they are equal and equally important. However, some legislators wield more influence than others because they are in the majority, or because they are very experienced and can understand politics and public policy well.
Some committees are more important than other committees.
For example, the Senate Finance Committee and the Assembly Ways and Means Committee are the primary committees which influence the budget process. It is those two committees that fashion responses to each step of the budget process. The fiscal committees of the Legislature are arguing with each other about the total amount of money available for the State to spend in the coming fiscal year. Once they reach agreement on that figure, and they are supposed to do so by March 10, they will decide how the spending will break down, category by category. This is supposed to happen by April 1.