Update: The Canon Hand Strap E1 has been discontinued. The Canon Hand Strap E2 is available, but it uses a different method for connecting to the camera body (it connects to a camera using the tripod mount and neck strap loop).
Just as a neck strap keeps a camera attached to your neck, the Canon Hand Strap E1 keeps a camera attached to your hand.
A neck strap has a tendency to get in the way when it is not actively being used - and can even be the cause of a dropped camera if the strap catches on something unexpectedly. If you are going to be primarily holding the camera in your hand, it may make more sense to use a hand strap. The hand strap helps control and support the camera - and helps prevent it from falling to the ground.
The Canon Hand Strap E1 requires a 1-Series body or a battery grip for attachment. However, hand straps including the E-1 do not provide portrait grip support. So you need to add the weight and bulk of a portrait/battery grip to a non-pro body for no other reason than to attach the E-1? Well, you still get the extra battery and you can still use the vertical grip - but not with the handstrap. There is a battery grip alternative - the CamAdapter.
The quality of the Canon Hand Strap E1 is reasonable but not excellent. It is priced accordingly.
I found the E-1 to provide minimal support as it is somewhat "rolly" with its 2-point attachment. The Nikon AH-4 Handstrap is a much nicer solution.
As I shoot a high percentage of my shots in portrait orientation, handstraps do not benefit me much.
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