  Like other young stellar objects (YSOs), FU Ori-type stars have been detected
as strong X-ray emitters. However, little is known about how the outbursts of
these stars affect their X-ray properties. We assemble available X-ray data
from XMM Newton and Chandra observations of 16 FU Ori stars, including a new
XMM Newton observation of Gaia 17bpi during its optical rise phase. Of these
stars, six were detected at least once, while 10 were non-detections, for which
we calculate upper limits on intrinsic X-ray luminosity ($L_X$) as a function
of plasma temperature ($kT$) and column density ($N_H$). The detected FU Ori
stars tend to be more X-ray luminous than typical for non-outbursting YSOs,
based on comparison to a sample of low-mass stars in the Orion Nebula Cluster.
FU Ori stars with high $L_X$ have been observed both at the onset of their
outbursts and decades later. We use the Kaplan-Meier estimator to investigate
whether the higher X-ray luminosities for FU Ori stars is characteristic or a
result of selection effects, and we find the difference to be statistically
significant ($p<0.01$) even when non-detections are taken into account. The
additional X-ray luminosity of FU Ori stars relative to non-outbursting YSOs
cannot be explained by accretion shocks, given the high observed plasma
temperatures. This suggests that, for many FU Ori stars, either 1) the outburst
leads to a restructuring of the magnetosphere in a way that enhances X-ray
emission, or 2) FU Ori outbursts are more likely to occur among YSOs with the
highest quiescent X-ray luminosity.
