Are fresh baby carrots better than full sized carrots?

Same: The "baby carrots" sold in stores are regular, fully-grown carrots cut into those little shapes. They're not "baby"-- that's just a marketing term. If buying carrots cut and clean and in little shapes makes it more likely that you are your kids will eat them, go for it!

Not necessarily: "baby carrots" are actually regular carrots which have been trimmed to resemble baby carrots. There is no health difference but there may be a convenience difference.