  We study and compare the discovery potential for heavy neutral gauge bosons
($Z'$) at various $e^+e^-$ and $p\stackrel{(-)}{p}$ colliders that are planned
or have been proposed. Typical discovery limits are for the TEVATRON $\sim 1$
TeV, DI-TEVATRON $\sim 2$ TeV, LHC $\sim 4$ TeV, LSGNA (a 60 TeV $pp$ collider)
$\sim 13$ TeV while the $e^+e^-$ discovery limits are $2-10\times \sqrt{s}$
with the large variation reflecting the model dependence of the limits. While
both types of colliders have comparable discovery limits the hadron colliders
are generally less dependent on the specific $Z'$ model and provide more robust
limits since the signal has little background. In contrast, discovery limits
for $e^+e^-$ limits are more model dependent and because they are based on
indirect inferences of deviations from standard model predictions, they are
more sensitive to systematic errors.
