With old cameras, you had film with fixed ISO and you could bracket your shots by either adjusting the f-stop or exposure time. Normally, if I have enough light, I prefer to keep the f-stop constant and wide open. I'm wondering with digital cameras what effect I get by instead bracketing the ISO setting instead of the exposure time? Why would I prefer one over the other or is there no real difference in the resulting photographs I would get? Assuming blurring is not an issue it it better to change the exposure time and keep ISO constant?
This will create images with different amounts of noise in them. I call this grain, others just call it noise. Depending on the ISO range that you are using, you may or may not cause issues by doing this. Higher in the range, if you combine different areas of a ISO bracketed image you will see different noise profiles throughout and that may be undesirable.
This will give you images that are taken for different amounts of time. This could give you issues if you are concerned with speed because of movement in the image, such as if a car or person is in the shot. It also can cause issues if you are hand holding the camera. If the shutter speed becomes so slow that you introduce blur into the shot from your hand movements, then that would be a concern.
I wouldn't call one solution better or worse, it all depends on the situation and what your desired output is. If you are in a low ISO range already, bracketing will have few downsides. If you are in a fast shutter speed range already, bracketing will have few downsides. It is when you are in the upper limits of each that you have to chose what trade offs you are comfortable with.