distance between histograms
If you normalize your histograms you then have an empirical pmf. There are numerous methods to calculate distances of pmfs, such as Kullback-Leibler and Jensen-Shannon divergences. If the base-set of the histograms are exactly the same then KL divergence will work fine. If they intersect, but are not exactly the same, then JS divergence will work instead.

Be careful as KL divergence is non-symmetric. That is, given two pmfs $P$ and $Q$, $\text{D}_{\text{KL}}(P||Q)$ may not be equal to $\text{D}_{\text{KL}}(Q||P)$. On the other hand $\text{D}_{\text{JS}}$ is symmetric, but still not a metric.