USB 3.0 max current is 0.9k mah. Your wall charger is 2.0kmah(ipad charger current). So it charges at less than 1/2 the speed of the wall charger. Most of the older wall charger outputs at 1.0kmah(iphone charger current). And usb2.0 charges at 0.5kmah. You also may not get max speed as your computer USB ports may be sharing the current with other device etc especially when using usb hub. Best to get a powered USB hub to ensure full current when connected using the computer.
The galaxy charging current app is able to show input current to your samsung phone
https://play.google.com/store/apps/details?id=com.abmantis.galaxychargingcurrent.free&hl=en
Yeah I know about the current thing, but the problem you see, I believe it's the bad optimisation between Android 4.3 or Snapdragon S800 eating too much battery while using.
I charged my Note 2 via USB 2.0 cable, it's going up
I charged my Note 3 via USB 3.0 cable, it's going down, slowly
Given the battery capacity difference by only a little, the only way I think it's the Snap S800 eating too much battery, as well as the 1080p screen.
I hate it when I can't charge my Phone via USB desktop, even with USB 3.0...