Not sure there is any such thing as a "regular 6mm". The three most likely to be compared are the 6mm Remington which I believe is basically a necked down 257 Roberts, the 243 Winchester which is a necked down 308 Winchester, and the 6mm Creedmore which is a necked down 6.5 Creedmore. While it had a good beginning, the 6mm Remington never really got off the ground because the original was twisted too fast (1 in 12") for a decent deer bullet at the time it was released. Remington re-released it with a 1 in 9 with the introduction of the Remington 700 rifles but it was too late.
The 243 has always been king of the 6mm hill. If you don't know what that is, then I probably can't help you.
The 6mm Creedmoor was based on the 6.5 Creedmoor, and that round is a slightly smaller twin to the 260 Remington which is a necked down 308. The 6.5 Creedmore case is essentially the 260 Rem. case with the shoulder pushed back a bit to lengthen the neck. The shoulder is sharpened from 200 to 300. The result is internal volume about 5% less than the 260 Rem, but less bullet intrusion into that powder space. In the average rifle, the 260 will drive 140-grain bullets about 50 fps to 100 fps faster than the 6.5 Creed. Similarly, the average 243 will drive a 90-grain bullet 100 to 150 fps faster than the creed.
However, both creeds come equipped with a magic fairy dust that dulls the brains of anyone who owns one. After holding a Creedmore cartridge in their hands and chambering it, it somehow gains a thousand feet per second, shoots under a tenth of an inch, and actually stops dropping totally so those who own them don't have to hold for distance or wind. They just aim and shoot from 50 to 5000 ft.
If you buy a creed, get a gas mask to prevent fairy dust from contaminating your brain. Or, don't get the gas mask, join the horde of brainwashed Creed lovers, and then entertain us all with how awesome it is.