IS/VR will reduce camera shake, but it will not stop action or motion blur.
For example, say you're shooting with a 1.6x crop camera at 50mm (same angle-of-field as 80mm in film or full-frame digital). In general, if you shoot handheld, you can expect the shot to be free of shake most of the time when you shoot at 1/50 sec or faster. With newer IS/VR lens, you can expect to get shots 3 stops slower. Meaning about 1/6 sec.
That is very useful for night scenes. But if you're shooting moving subjects - birds, cars, kids - those subjects will move a lot in that 1/6 sec. Your static background will likely to be free of motion blur, but the subject will still have moved.
BTW, if you go with Canon, the 50-250 is a newer lens with better optics, in additional to IS. It's a superior lens to the 75-300III whether you use IS or not.