In which cases is the Clemmensen reduction is preferred over the Wolff-Kishner reduction?
One thing is that the Clemmensen reduction is done under acidic conditions whereas the Wolff-Kishner reaction is done under basic condition, and that I think decides somewhat which to choose depending of the nature and other groups present in the reactant.
But are there any other points to keep in mind while choosing the best suitable reaction?
A key consideration for the Wolff-Kishner reduction is thermal stability of the substrate. High temperature is required for the classical reaction using hydrazine and KOH, sometimes up to 200 °C. This can rule out plenty of compounds.
The Clemmensen reduction may be fine for the laboratory, but fundamentally many industries wouldn't use it due to scaling up the use of mercury.
Scalable alternatives are molecular hydrogen with a catalyst under acidic conditions or, the trifluoroacetic acid-silane combination, such as triethylsilane or tetramethyldisiloxane.
The basic difference is the medium as Clemenson is in acidic medium so if $\ce{OH}$ is present so it will be attacked too, but in Wolf-Kishner it is in basic medium so $\ce{OH}$ group can be saved which is sensitive, but if there is halogen, ester, or amide group it will not tolerate the reaction.
