I've not worked at all with the .375 JDJ, but as I understand it's a .444 Marlin case, necked down to take the .375" bullets, and develops about 2,400 ft lbs of energy. It has been very successful over the years as a hunting cartridge. I believe a 270 gr bullet does about 2,000 fps from the JDJ, although that may well be from a handgun, not a rifle.
The .375 H&H has been around for nearly 100 years and is a larger cartridge, one of the original belted magnums. Typical factory and hand loads for the .375 develop around 4,000 - 4,500 ft lbs of energy. A 270 gr bullet does about 2,700 fps from the H&H, and shoots with a trajectory very similar to a 180 gr .30-06 load.
I'm normally not big on using "energy" figures but it seemed an easy way to make the comparison. They're both good cartridges. I handload for the .375 H&H, and started hunting with it (Ruger Number One) a couple of years ago. So far, I'm impressed with the cartridge. Excellent accuracy and power, and not half bad to shoot, at least not from my rifle. No wonder it's still around after all this time.
Regards, Guy