  It is well known that quasi-local black hole horizons depend on the choice of
a time coordinate in a spacetime. This has implications for notions such as the
surface of the black hole and also on quasi-local physical quantities such as
horizon measures of mass and angular momentum. In this paper, we compare
different horizons on non-spherically symmetric slicings of Vaidya spacetimes.
The spacetimes we investigate include both accreting and evaporating black
holes. For some simple choices of the Vaidya mass function function
corresponding to collapse of a hollow shell, we compare the area for the
numerically found axisymmetric trapping horizons with the area of the
spherically symmetric trapping horizon and event horizon. We find that as
expected, both the location and area are dependent on the choice of foliation.
However, the area variation is not large, of order $0.035\%$ for a slowly
evolving horizon with $\dot{m}=0.02$. We also calculate analytically the
difference in area between the spherically symmetric quasi-local horizon and
event horizon for a slowly accreting black hole. We find that the difference
can be many orders of magnitude larger than the Planck area for sufficiently
large black holes.
