We study the X-ray luminosity function (XLF) of low mass X-ray binaries (LMXB) in the nearby early-type galaxy Centaurus A, concentrating primarily on two aspects of binary populations: the XLF behavior at the low luminosity limit and comparison between globular cluster and field sources. The 800 ksec exposure of the deep Chandra VLP program allows us to reach a limiting luminosity of 8e35 erg/s, about 2-3 times deeper than previous investigations. We confirm the presence of the low luminosity break in the overall LMXB XLF at log(L_X)=37.2-37.6 below which the luminosity distribution follows a constant dN/d(ln L). Separating globular cluster and field sources, we find a statistically significant difference between the two luminosity distributions with a relative underabundance of faint sources in the globular cluster population. This demonstrates that the samples are drawn from distinct parent populations and may disprove the hypothesis that the entire LMXB population in early type galaxies is created dynamically in globular clusters. As a plausible explanation for this difference in the XLFs, we suggest that there is an enhanced fraction of helium accreting systems in globular clusters, which are created in collisions between red giants and neutron stars. Due to the 4 times higher ionization temperature of He, such systems are subject to accretion disk instabilities at approximately 20 times higher mass accretion rate, and therefore are not observed as persistent sources at low luminosities.