The light novel doesn't give specific differences, but Shin says that the maximum stats of a regular human is in the mid-300s, which isn't good for fighting monsters. Shin reincarnated multiple times in the game and was able to raise his stats that way, but the exact method for reincarnation is unkown. Wolfgang and Cuore are high beasts so one can be born as a high race in the new world. Both of them have higher than average stats with Wolfgang being one of the strongest in the beast tribe.
What is known is that high humans have a lifespan of 150 years, so we can assume that the other high races live longer.