To fix the 'Cannot Download' problem with Destiny update 1.29 you need 50Gb of free space on your PS4 hard drive to begin installing the update. Tested this myself by removing files until I had over 50Gb of free space and the update began installing immediately.
Either Bungie or Sony needs to fix this. Can't vouch for XB1 but if the same issue occurs the fix is probably the same.
Cheers
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Edit: This fix is for the 'Cannot Download' problem. If you're 'Preparing to download' is stuck at 10% that is not the same issue.
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I have almost seventy GB of storage left and it isn't working. It's going to three percent and then stopping immediately and saying cannot download. Should I rebuild the system database? It doesn't wipe the system, it just rebuilds corrupted data.