  We conduct one of the largest systematic investigations of bright X-ray
binaries (XRBs) in both young star clusters and ancient globular clusters (GCs)
using a sample of six nearby, star-forming galaxies. Combining complete CXO
X-ray source catalogs with optical PHANGS-HST cluster catalogs, we identify a
population of 33 XRBs within or near their parent clusters. We find that GCs
that host XRBs in spiral galaxies appear to be brighter, more compact, denser,
and more massive than the general GC population. However, these XRB hosts do
not appear preferentially redder or more metal-rich, pointing to a possible
absence of the metallicity-boosted formation of low-mass X-ray binaries (LMXBs)
that is observed in the GCs of older galaxies. We also find that a smaller
fraction of LMXBs is found in spiral GC systems when compared with those in
early-type galaxies: between 8 and 50%, or an average of 20% across galaxies in
our sample. Although there is a non-negligible probability of a chance
superposition between an XRB and an unrelated young cluster, we find that among
clusters younger than 10 Myr, which most likely host high-mass XRBs, the
fraction of clusters associated with an XRB increases at higher cluster masses
and densities. The X-ray luminosity of XRBs appears to increase with the mass
of the cluster host for clusters younger than ~400 Myr, while the inverse
relation is found for XRBs in GCs.
