True or false: Wide-angle lenses give you greater depth of field (DOF) than long lenses. It's false. Focal length has something to do with DOF, but only indirectly.
In any given film or digital format, depth of field is instead determined by subject magnification-how big the subject appears in relation to the size of the piece of film (or the digital imager). An image of a 1x1.5-inch postage stamp that fills the 1x1.5-inch frame of 35mm film is at 100 percent or 1.0X magnification (life-size). An image of a bull moose, 100 inches from hoof to rack, filling a 35mm frame, is around 0.01X.
So, the DOF of a 20mm lens is the same as the DOF of a 200mm lens, given the same f-stop and magnification. Period.
OK, here's the rub: For the 20mm lens to produce the same magnification (of, say, your cat) as a 200mm lens, you'd have to hold the 20mm in Kitty's face and the 200mm way across the room. So, for practical purposes, it's easier to limit DOF with a tele and to expand DOF with a wide-angle. But you can get shallow depth with a wide-angle, and deep depth with a tele; it just depends on where you stand.
Here's the other rub: Where you stand also affects the perspective of the picture. The 20mm lens in Kitty's face makes for a funny image-the typical big-nose look. Move back and shoot with the 200mm, and the perspective flattens out.
This is why, if you want to limit depth of field in a facial portrait, you don't use a 20mm lens at f/2.8 in your subject's face. You move back and fill the frame using a telephoto lens at f/2.8. You'll get the same DOF (because you're using the same magnification and f-stop), but drastically different apparent perspective (because you've moved back).