Thinking about getting the Extra Pack 1 for the USCG HC-130 but I honestly don't understand what the difference is between this model and the base C130 with a USCG repaint? What is different on it?

These are different models. Base Pack has C-130E, Extra Pack has HC-130.

Right, I know that. What I don't understand is what is different about the two models. From looking at pictures the HC-130 is just the C-130 with a USCG paint job.

I think the HC-130 has extra fuel tanks.

C130E's use GTC's, HC130's (17XX) use APU's. Also, different airconditioning packs.. Most operators of C130E's probably wouldn't care about the weaker AC pack on the E's, but an HC130 will spend a ton of time flying at low altitudes to do  search and rescues.....were the E's AC pack will do nada for keep the temps cool. I flew on a few 15XX's with the old AC packs while running the sensory gadgets, even stripped down to my skivvies, I was stil sweating my tushy off....note the 15XX are truely E's, although some were upgraded with better AC packs off the 16XX from Hawaii that were retired early because of corrosion issues, but reguardless...15XX were put in E-City for a reason.....it's much cooler there.