Black holes and wormholes are solutions of Einstein's field equations, both of which, from afar, can look like a
central mass. We show here that although at large distances both behave like Newtonian
objects, close to the event horizon or to the throat, black holes and wormholes have
different tidal effects on stars, due to their respective geometries.
We quantify this difference
by a numerical procedure in the Schwarzschild black hole and the exponential wormhole backgrounds,
and compare the peak fallback rates of tidal debris in these geometries.
The tidal disruption rates in these backgrounds are also computed. It is shown that these quantities are
a few times higher for wormholes, compared to the black hole cases.