$\exists \text{ symbol favors } \vee$ whereas $\forall \text{ symbol favors } \wedge$
P1: $\exists x (\neg P(x)) \vee \exists x (Q(x))$
P1 will be true if there is no $x$ for which $P(x)$ is true or there is some $x$ for which $Q(x)$ is true.
P2: $\exists x(\neg P(x) \vee Q(x))$
P2: will be true if either Q(x) is true or there is no $x$ for which $P(x)$ is true
So both the statements mean the same and hence are same.