Why is iPhone Software Update twice as large in iTunes than on iPhone
iTunes does not download the same file as your device does.

When you download the update/upgrade directly to your device, you are downloading a delta update. This means that only the parts of the system which have changed are downloaded, and the rest is left the same. Updates are downloaded this way to reduce the download size.

iTunes could also download a delta update, but doesn't because it saves the downloaded data for later. Instead, it downloads the entire firmware image. There are two reasons to do this. First, you can use your computer to update another device, which could be running a different version of iOS. If it only downloaded a delta update, then it would need to perform a second download for the other version, since there may be different parts of the system which have changed. With the entire firmware, it already has everything it needs (provided that the two devices are the same model, so they use the same firmware). Secondly, you can use iTunes to restore a device which is not working. During a restore, the entire image must be written, since it is not known what parts need to be replaced, so a delta update could not be used.