Exposure delay is mainly for reducing vibration caused by the camera itself—especially mirror movement, and sometimes shutter/button-press vibration. It can help whenever you can tolerate the delay, but it’s most useful in situations where tiny vibrations matter, such as tripod-mounted work, macro, or other high-magnification shots.

VR/image stabilization addresses a different problem: movement by the camera/lens system during the exposure. So the two can be complementary—less vibration going in generally gives stabilization a better chance to work.

However, if the camera is on a tripod, VR is often turned off because some stabilization systems can introduce blur when the camera is already steady. Some systems handle tripod use better than others, so testing your setup is wise.

For handheld shooting, exposure delay may still help if pressing the shutter causes noticeable shake, but subject movement and normal hand movement usually matter more than mirror vibration.

In short: use exposure delay when you want maximum sharpness and can afford the timing delay; use VR mainly for handheld shooting, and usually disable it on a tripod unless your system is known to work well there.