When the Note 3 first came out the talk of the USB 3 cable and port charging faster was all the rage. However, the only portion of the USB 3 connection that can be used for charging is the USB 2 portion. There was a UTUBE video by one of the android writers where he actually tried charging the same Note 3 phone from the same power source and found that until about the 95% charged level (if memory serves) the charging rate was identical (as should be expected since the new portion of the USB 3 connection only carries data). The last few percent of charge does indeed go faster but this was attributed to the charging software as the hardware, of course, didn't change during the charging cycle.
That said, the specs for the Note 3 list a minimun input amperage for charging as 1.3 amps. This is higher than the older PCs, wall chargers, and car chargers output.