The 501st were regular troopers, just another Legion, but they built up extreme experience during the clone wars, especially under Rex and Anakin. Throughout Anakin's, and later, Vader's, lifespan, the 501st was committed to Jango clones only, while the other clones were stuck with the "inferior" non-clone new recruits. Hilariously, Commander Cody complains greatly over this predicament, correctly calling the new recruits "inferior", and thus, ruining GAR's reputation. This is true. In the original trilogy, we see troopers being blasted to bits by the droves, and in video games such as The Force Unleashed, Galen Marek cuts through them like cordwood.
The 501st Legion was the longest lasting and most feared and prominent sect of clone troopers in history, lasting from 21 BBY to approx. 137-9 ABY, maybe longer. After the Clone Wars the 501st were the most consistent in the Stormtrooper army. After the near total destruction of Palpatine's Empire, the 501st switched loyalties to the Fel Empire.