Here's the scenario: every so often our garden plays host to some small deer. Naturally, I try to take pictures of them. From inside the house, I can get a decent shot with full zoom on my camera. The difficulty is that the kids also like to see the deer and one particularly wriggly child needs to be lifted up to be able to see them. So sometimes I'm trying to take a picture one-handed with a wriggly child in the other arm. Not the best conditions for a steady shot!
My camera has enough resolution that I could take a photo with a lower zoom factor and then crop it later and still have enough detail for a decent photograph. So, given the above circumstances, which is going to provide me with the least blurred photograph: full zoom or least zoom with later cropping (which is what I mean by "digital zoom" in the title of the question)? Note that I'm only interested in the blur on the deer itself, I don't care about the rest, and (for the purposes of this question) I want to focus (ha ha) on blur from camera shake.
Also, due to having small child under one arm, in this circumstance I have the camera on "P" mode, letting it select the best aperture and shutter speed. I guess that this might make a difference.
Answer
Assuming you crop to the same area and print to the same size, the amount of camera-movement blur should be indistinguishable between the two cases. Using a shorter focal length will decrease the impact by exactly the amount you have to crop and enlarge.
So, it comes down to other factors. The most important (from the narrow viewpoint of camera-shake blur) may be that your zoom lens may allow a wider aperture at shorter focal lengths, which would let you speed up the shutter, reducing blur.
But in real use, I don't think that's necessarily going to make up for the decrease in resolution.
I think what I'd do is ask the kids to let you take turns taking pictures and holding them. They'll appreciate looking at the pictures, too.
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