iPhone available space: significant difference between iTunes and iPhone

I am trying to update my wife's iPhone from ios 7 (.x.x) to 8 (the latest). I was trying through iTunes because the iPhone says only around 300MB is available. iTunes shows around 7GB as available space. But when I hit update, it complains that at least 770MB should be available and it is not.

Is this a known issue that iTunes reports a larger available space than iOS? I have read about the "Other" storage space problem, but this is about "Free" space.

Also, is there a workaround to reclaim this "free" space?

This is a iPhone 5S, latest iTunes (12.0.1.26) on OSX Yosemite (10.10.1)

iPhone:

iTunes: