The new carrot colors are far from new, the first carrots were purple, white and yellow. Orange was the unique variety that got cultivated widely hundreds of years ago. The orange color is the result of Dutch cultivation in the 17th Century, when patriotic growers turned a vegetable which was then purple into the color of the national flag.
Purple carrots have up to 28 times more anthocyanins, than orange carrots. Black Carrots also contain anthocyanins, flavonoids have anticancer compounds, they are free radical scavengers in living systems, as well as inhibitors of LDL (the bad) cholesterol and the black carrot anthocyanins are especially active.
We have not yet planted black carrots, haven’t seen the seeds for them. I am wondering if they look very appetizing. The purple carrot, we noticed, are not always purple all the way through. Some have yellow or orange insides, but some are deep purple the whole way. The "Deep Purple", I think, are uniformly colored the whole way through. It was disappointing when we first planted purple carrots to find that the variety we planted had only the thinnest layer of purple on the outside and if you peeled them they were orange!
Yellow carrots are rich in Xanthophylls, similar to beta-carotene, they are linked to eye health and may reduce the incidence of lung and other cancers.
Red carrots are rich in Lycopene, found in, is a type of carotene also found in tomatoes. It is believed to help prevent heart disease and, in conjunction with other phytochemicals, reduce the risk of certain cancers.

Purple carrot varieties: Indigo, Maroon, Purple Dragon, Cosmic Purple,
Purple Haze
Yellow Carrots: Sunlite, Solar Yellow, Yellowstone,
White Carrots: Creme De Lite, White Satin
Red Carrots: Supreme Chateney, Red Samurai
Black: Black Knight, Indigo