Stabilization is a wonderful aid, but not as a substitute for a tripod. When you can use a tripod, you’ll get sharper results that way than shooting handheld with stabilization. Many serious wildlife photographers who use a really long lens (400mm and up) will use a gimbal head with their tripod. The gimbal holds the camera steadily, but allows you to move it in any direction to track your subject.
Can a stabilizer hold your camera as still as a tripod? No way. But if you work handheld, a stabilizer will give you sharper shots at slow shutter speeds than you’d get without stabilization. It’s that simple.
Now that an ever-increasing number of DSLRs can shoot video, you may wonder if stabilization can help you get steadier videos. Yes and no. DSLR stabilization systems were designed to help you hold the camera steady during a relatively brief exposure. They weren’t designed to keep a camera rock-solid for video clips of several seconds or even minutes. So, yes, the stabilizer provides for steadier handheld video shooting, but any shake at all in a video is very distracting to the viewer, so videos should be shot from tripods unless you want a handheld effect.
Also, the stabilizer makes a soft sound, which a video-capable DSLR’s built-in microphone will pick up. If you’re shooting without sound, or using an external microphone, this isn’t a problem, but it’s best not to use the stabilizer (or change any camera settings while shooting) when using the built-in microphone.