No, there is no difference. Notice that if $v$ is an eigenvector to $A$ with eigenvalue $\lambda$ and $\alpha$ is a scalar, then
$$ A \alpha v = \alpha A v = \lambda \alpha v $$
and thus $\alpha v$ is also an eigenvector with eigenvalue $\lambda$. Since $\alpha$ is any scalar, if you let $\alpha = -1$ then you see that $v$ being an eigenvector implies $-v$ is an eigenvector. So there is no mathematical difference between which "scaling" of the eigenvector you choose ($\alpha$ just scales the eigenvector and flips it).
Note: Normally one chooses the normalized eigenvalue (norm = 1) but even then that doesn't account for the "flipping".