The output capacitor is crucial for stability and high frequency regulation, the input capacitor protects the
regulator against voltage spikes, it normally doesn't have to be large as its not acting as a reservoir.
Spikes/noise on the input can directly affect the amplifier circuitry in the regulator, ie the input capacitor is
decoupling for this amplifier (linear regulators are basically error amplifiers).
My intuition is that if the input supply to the regulator is not stiff (ie comes in on long wires perhaps,
or is a PV panel), then the input cap should be large too.