Turns out the big expansive open world requires a smaller install on Xbox One than expected.
According to the product details page on Xbox.com, you will want to set aside 28.12 GB of space on your Xbox One hard drive in order to install Fallout 4. That amount of space, 28.12 GB, is certainly nothing to sneeze at, but I'm sure many (myself included) expected Fallout 4 to take up a much larger chuck of the Xbox One's hard drive.
The PlayStation 4 and PC install amounts have not yet been revealed. One number you won't necessarily need to worry about regarding Fallout 4, is your level cap because there isn't one. You can read more about that here.