The steel ball will have a higher momentum.
Momentum depends on the velocity and on the mass of an object according to the following relationship
In your case, you know that the speed of the steel ball is equal to the speed of the cotton ball, so you can write
You can establish a relationship between the momentum of the steel ball and the momentum of the cotton ball by dividing these two equations
However, you have no information about the masses of the two balls, but you know something about their volumes.
Mass can be expressed by using density and volume
Since you know that the two balls have equal volumes, you can write
Since the density of steel is bigger than the density of cotton, you have
Therefore, the steel ball will have the greater momentum if velocity and volume are equal.