iPad upgrade from iOS 8.3 to iOS 8.4 fails with Error 3004 - iPhone 5 upgrade worked perfectly on same computer

Today, 2015-07-01, I successfully upgraded my iPhone 5 from iOS 8.3 to iOS 8.4 via iTunes installed on my Windows 8.1 64-bit laptop.i

I then plugged in my iPad 3 into the same computer and attempted to upgrade it from iOS 8.3 to iOS 8.4, but near the end of the process, I get a pop-up error in iTunes that says Error 3004.

My question: why did the iPhone 5 upgrade work but the iPad 3 upgrade fail, using the exact same computer and the exact same internet connection?