Is there anything pcolor can do that pcolormesh can't?

Until very recently, I had somehow wound up with the impression that pcolormesh only handles rectilinear coordinate arrays, while pcolor can handle arbitrarily shaped quadrilaterals.

Apparently, both pcolor and pcolormesh can handle any type of quadrilateral. For example:

import numpy as np
import matplotlib.pyplot as plt

y, x = np.mgrid[:10, :10].astype(float)
x += 0.5 * np.random.random(x.shape)
y += 0.5 * np.random.random(y.shape)
z = np.random.random(x.shape)

fig, axes = plt.subplots(ncols=2)
axes[0].pcolor(x, y, z)

axes[1].pcolormesh(x, y, z)

Given that, is there any effective difference between pcolor and pcolormesh other than that pcolor creates a PolyCollection and pcolormesh creates a QuadMesh?

In other words, is there anything that pcolor can display that pcolormesh can’t?