Comparison of Strong OPerator and Weak * Topologies on B(H)

Question

It is known that in $\mathfrak{B}(\mathbb{H})$, the weak operator topology (WOT) is contained in both the strong operator topology (SOT) and $\sigma$-weak topology. In general the SOT and the $\sigma$-weak topology cannot be compared. To prove this we must show that each contains some set that the other does not. Does it suffice to show that there exist functions that are continuous with respect to one topology but not the other?