When it comes to bad broccoli, you can't beat Outback . . . I mean seriously, you get mostly stalk with some little numbs of the flowerettes on the tips.
But broccoli is really iffy . . . I find that when it comes to broccoli, it needs to be enhanced for my tastebuds. If it's raw broccoli, it needs some kind of dip; if it's cooked broccoli, it needs some salt and maybe a little melted butter as well.
Carrots I think I tend to like a little better raw than cooked, but when it comes to cooked carrots, there's usually two different kinds in my house: sweet or savory. By that I mean the carrots are either roasted in a mixture of brown sugar and syrup of some kind, or roasted with seasonings like garlic salt or onion powder. But like fuzzygobo said about broccoli, it's hard to cook carrots just right: if they're undercooked, they still have too much bite to them; if they're overcooked they're practically mush.