Not much more to add:
Both sodium percarbonate and sodium perborate are oxygen bleaches, that is they give up hydrogen peroxide in water which is what does the actual bleaching.
Sodium perborate has been the standard for oxygen bleaching on both sides of the pond for ages. It is inexpensive, stable in formulations, and has a few other properties due to it's being derived from borax. However sodium perborate is called the "hot water" oxygen bleach, because it requires temps >120F to really get going, with >140 preferred. However this problem was solved by adding bleach activators (TAED and NBOS are the most common), which allows "boil wash" bleaching results in water temps of 140F to 100F. Both P&G and Henkel Germany have numerous patents on activated oxygen bleaching systems, and are part of their top shelf detergents such as Tide and Persil.
Because sodium perborate is not that active of a bleach in warm or cold water (though like all oxygen bleaches it will work, it just takes a very long contact time), it is frequently used as a "colour safe" oxygen bleach. This is because at the water temperatures colours are normally laundered, there is less risk of damage. Rule to remember is that for about every 10 degree temperature increase, there is an 18% increase in bleaching action. So what is safe at 100F may bleach out colour at 140F or 160F.
Sodium Percarbonate is the "cold water" oxygen bleach, in that it is active in warm and cool water without the requirement for bleaching activators. Uncoated sodium percarbonate is rather unstable, and looses power over time, which lead to the development of coated versions to produce more stable versions to give longer shelf life, especially when combined with detergents.
Though not necessary, some commercial detergents do combine a bleaching activator with sodium percarbonte both to enhance cooler water bleaching,and stain removal, but for another reason as well.
When both sodium perborate and sodium percarbonate are combined with bleaching activators they produce a chemcial compound called peracids. Peracids not only powerful bleaches, but very effective disenfectants as well. Brewers who do not use chlorine bleach to disenfect their equipment (for obvious reasons), do use peracid based cleaners. There are even commercial laundry detergents/oxygen bleaches sold in Europe that are certified to disenfect laundry with proper dosage of chemical and water temps of 140F held for a certian period of time.
Because of the bleaching activators, some oxygen bleach containing detergents such as Tide or Persil have been said to cause fading of darks and some colours, even when using warm and cool water. Hence the reason Persil has "Persil for Colours" and P&G sells Cheer.
In Europe, detergents with oxygen bleaches serve many other purposes as well, including helping to control the growth of germs and mould inside the washing machine. Indeed many European washer repair persons blame the recent outbreak of mould, slime and foul odours in front loaders on a mix of several factors, including use of mainly warm to cold water for washing, and using less to none bleaches (in Europe bleaches most always refers to oxygen bleach, LCB is called various things such as eau de Javel and is rarely used for laundry).