Samsung has confirmed via sammobile, that the Note 3 to be officially unveiled on 4th September, will indeed start at 32gb minimum internal storage. The 16gb model is being completely dropped. It will also be available online at a high price at the end of September.
Currently the Samsung Galaxy S4 32gb has approximately 23gb free, so expect the Note 3 to be around that mark, or even lower due to all the S-Pen software.
The Note 3 is turning out to be a cracking device.