I've used all three extensively on some species and sparingly on several more. The results are species specific. Generally, the vast majority of mammals don't noticably react to red and IR lights, while many do react to green lights.
Species specific responses I've observed:
Deer: No reaction to red or IR light. Always react to green light. Green light seems to always make them see their shadow and spook.
Raccoon: No reaction to red or IR light. Often reacts to green light, but then often relaxes and ignores it. Rarely they will spook off from a green light.
Bobcat: No reaction to IR light. Usually no reaction to red light, but sometimes they will look up when a red light is turned on, but never does it spook them. Cannot rule out that they are reacting to movement or sound instead of the light. Green light is unknown.
Possum: No reaction to red or IR light. Green light is unknown.
Rabbit: No reaction to IR light. Sometimes reacts and spook to intense red light. I cannot clearly recall green light reactions, although I vaguely think I remember them consistently spooking.
Hog: Often no reaction to red or IR light, but I've seen a hog on one occasion with each kind of light to apparently notice and spook at both. On the one occasion I saw a hog spook at a "red" light, the light was actually pink intead of true red. With the IR, it only spooked when very close. I have the impression at close range the hog can see the glow of the IR array. Green light is unknown.
Fox: No reaction to red light in years past while seeing foxes while coyote hunting. I've only recently started fox hunting. I did have one spook recently when I clicked a red light on, but that might have been it reacting to the sound of the light switch clicking. On two other occations a fox completely ignored a very intense red light. Concerning IR, I am convinced the fox can see it. On several occations over the past few weeks I've watched a fox at close range ignore me with a red light and spook when the IR was turned on. I've also watched it shield its eyes from the IR beam. Green light is unknown.
Beaver: No reaction to IR. Red and green is unknown.
Rats: No reaction to red or IR. Green is unknown.
My general thoughts are that for a cheap solution, red light is your best bet. I haven't tried green light on as many animals as red or IR, but every animal I have tried it on definitely sees it. IR is good but can be expensive and clunky because you must use a scope or camera that can see it. At the very least it makes you depend on lots of batteries. I've ruined hunts because I've went afield with low batteries in my IR scope and camcorder.