  We present the X-ray luminosity function (XLF) of low mass X-ray binaries
(LMXBs) in the globular clusters (GCs) and fields of seven early-types
galaxies. These galaxies are selected to have both deep Chandra observations,
which allow their LMXB populations to be observed to X-ray luminosities of
$10^{37}-10^{38}$ erg/s, and HST optical mosaics which enable the X-ray sources
to be separated into field LMXBs, GC LMXBs, and contaminating background and
foreground sources. We find that at all luminosities the number of field LMXBs
per stellar mass is similar in these galaxies. This suggests that the field
LMXB populations in these galaxies are not effected by the GC specific
frequency, and that properties such as binary fraction and the stellar initial
mass function are either similar across the sample, or change in a way that
does not effect the number of LMXBs. We compare the XLF of the field LMXBs to
that of the GC LMXBs and find that they are significantly different with a
p-value of $3\times10^{-6}$ (equivalent to 4.7$\sigma$ for a normal
distribution). The difference is such that the XLF of the GC LMXBs is flatter
than that of the field LMXBs, with the GCs hosting relatively more bright
sources and fewer faint sources. A comparison of the XLF of the metal-rich and
metal-poor GCs hints that the metal-poor GCs may have more bright LMXBs, but
the difference is not statistically significant.
