From The TimeSplitters Wiki

The Revolver is the most damging pistol in Future Perfect, but that comes with a slow fire rate. It is similar to the Garrett Revolver and is found in the mansion series of levels (Mansion of Madness and What Lies Below ) of Future Perfect. The need in the first of the two is pretty much short lived because not much later, you find the shotgun. The Reload time can be cut short slightly by pressing the trigger multiple times while reloading--shaves a good half second, and helps to spring back in crowded situations quickly.

Despite that the shotgun has more power in the story levels, some people might find that the revolver is the safer choice for portions of the levels where there are abundant zombies (such as during "What Lies Below" when you need to save Jo-Beth) simply because of the higher clip size, and higher accuracy, making it easier to peg heads off in quick succession, and halt zombies before they can get within range to do any damage.