Wikipedia says the ranges are -
KC-390 with maximum payload (27000 kg*) = 1400
C-130J with max normal payload (34000 lb or 15400 kg) = 1800
Embraer says
KC-390 with maximum payload (23000 kg) = 1380
with 13000 kg = 2780
USAF says -
C-130H with maximum normal payload (16590 kg) = 1050
C-130J with maximum normal payload (15420 kg) = 1800
C-130H with 35000 lb (15875 kg) = 1300
C-130J with 35000 lb (15875 kg) = 1600
Lockheed Martin gives the same numbers for C-130J except that it doesn't specify a weight for 'maximum normal'
All distances in nautical miles.
It's hard to see how one can decide from those numbers that "the current C-130" (C-130H for the RNZAF, isn't it?) has a longer range than the KC-390. According to the official data, KC-390 can carry 23 tons further than the C-130H can carry 16 tons.
*Wiki cites a recent (March 2016) article on Defesanet by Pedro Paulo Rezende (Brazilian journalist), quoting Paulo Gastão, director of the KC-390 programme for Embraer.