If you look at the aircraft.cfg file you might find why you don't see any difference between the variants.   They all have the same settings no matter E, H, J (KC,HC,LC,AC)

[TurbineEngineData]
fuel_flow_gain=0.02
inlet_area=1.0
rated_N2_rpm=29920
static_thrust=158
afterburner_available=0
reverser_available=1

[turboprop_engine]
power_scalar=1.0
maximum_torque=19600     ;H:maximum_torque(23030)

Not really sure how they came about these configurations for the maximum torque but all the C-130 legacy (E,H) models should have the Allison T56-A-15 engines, and the J has the Rolls Royce AE2100-D3

When you compare the older T56 models with shaft horse power you can see the difference.
T56-A-7: 4,200 shp (3,133 kW)
T56-A-14: 4,600 shp (3,433 kW)
T56-A-15: 4,591 shp (3,425 kW)
T56-A-425: 4,600 shp (3,433 kW)
T56-A-427: 5,250 shp (3,920 kW)
T56-A-427A: 5,100 shp (3,806 kW)

The 2100D3:
Power:
AE 2100 A/P: 4,152 shp (3,096 kW)
AE 2100D2 and AE 2100D3: 4,637 shp (3,458 kW)
AE 2100J: 4,591 shp (3,423 kW)

In regards to what you are seeing on climb out the difference in settings may be a place you look at (19600 vs 23030) on the maximum torque.