Generally crystalline materials have higher photocatalytic activity due to reduced recombination of electrons. Amorphous semiconductors have a lot of trap states that cause a great loss in current. I would say monoclinic WO3 would have higher photocatalytic activity than the amorphous one but you would also need to look at things like the bandgap of both of them too.
Why do amorphous semiconductors have many trap states? what are they? do you mean for example oxygen vacavcy? oxygen vacancy can trap electrons and hence reduce electron-hole recombination. as a result we have more photocatalytic activity.
Not just oxygen vacancy. You can have dislocations of W atoms as well. Also the interactions between electrons and the ions will be different from one unit cell to another (imagining the amorphous film as a set of unit cells of slightly different lattice constants) and so on the average the motion of electrons will be totally random and the average displacement of electrons will be zero.
We have actually studied the trap states in amorphous and crystalline metal oxides (paper will appear soon) and we found that in the amorphous case, there are a lot of trap states that tend to be in the middle of the bandgap (it is well-known that midgap trap states tend to increase recombination). However, when we crystallize the film, most of these states disappear. Also, even if some of the electrons are de-trapped from the midgap states, this will increase the time needed for the electrons to reach the electrodes and hence reduce the collection efficiency.
You can imagine your electron as a balloon in the air in which the air molecules are hitting it randomly in all possible directions and so the net result would be that your balloon wouldn't drift in a certain direction. On the other hand, if the air molecules were arranged in a certain order, they will be pushing your balloon in a certain way and hence you will have a net displacement for your balloon. Does it make sense?