Orange carrots contain beta carotene, but purple carrots have more antioxidants & potentially more health benefits.
Some vegetables are as nutritious frozen as they are fresh, but not carrots. Peeling, processing, freezing, & thawing destroys much of their antioxidants.
Though convenient, baby carrots, pretrimmed & scrubbed, are actually misshapen mature carrots that have been whittled down to smaller, more uniform size. The part that’s thrown away, the outer skin & what’s just beneath it, is much more nutritious. As much as 1/3 of phytonutrients are lost by rimming away the outer parts.
Carrots are better for you when cooked. Cooking breaks down their tough cell walls, making their nutrients more bioavailable. And it matters how you cook them--boiling allows their water-soluble nutrients to leach into the cooking water. Steam or saute them instead. Also, cooking them whole instead of sliced or chopped retains more of their food value and natural sweetness. Cook first; then slice.
Eating carrots that have been cooked whole may even reduce cancer risks. Carrots contain falcarinol, a cancer-fighting compound. Whole cooked carrots have 25% more of it than those that have been cut before cooking.
Lastly, carrots are best eaten with a healthy fat or oil, because some of their best nutrients are fat-soluble.
(Eating on the Wild Side: The Missing Link to Optimum Health, by Jo Robinson. Little, Brown & Co., 2018)