While not wholly in favour of Fox hunting I can see no clear alternative. Having found a fox cub that was dying - slowly - from poison I am totally against that.
Shooting if in skilled hands yes, but amateurs are better not to try.
Hunting the fox either gets away or is killed mercifully quickly.
Stag hunting I can see no need for at all. Shooting will a skilled back up is fast and does not involve chasing a terrified animal all over the country side.