Why? More cutting means more surface area. And more surface area means more exposure to cooking water, which leaches out the carrot's nutrients. Among those nutrients is falcarinol, an anti-cancer compound.
That discovery should come as no surprise to anyone who's ever eaten carrots that have been boiled within an inch of their life: the more they're cooked, the less flavor they retain. So it follows that if flavor can be lost, so can nutrients.
The scientists who conducted the study at England's Newcastle University also made the connection between lost nutrients and flavor, noting that the whole-cooked carrots also tasted better because they retained more of their natural sugars.
Better health and better flavor: a win-win situation, cloaked in a flattering shade of orange.