Purely for scientific reasons, I ate these both in the same day some time ago.
Côte D'or milk chocolate with hazelnuts
Milka milk chocolate with hazelnuts.
Lets look at them unwrapped side by side, shall we?
left = Côte D'or, right = Milka.
As you can see, the Côte D'or bar is darker, which generally indicates a milk chocolate with higher cacao content. The flavour of the Côte D'or was certainly richer, but still very much a milk chocolate, meaning creamy and not bitter. Both bars were very sweet, though the Milka was definitely the sweeter of the two. Texture-wise, the Côte D'or was smoother, with the Milka coming across as a little bit 'waxy'. Last point: the hazelnuts. There is a very good flavour that comes through with the hazelnuts in the Côte D'or, they are perfectly roasted. With the Milka bar, the hazelnuts aren't very tasty at all.
As the price point for each bar is roughly the same (there has been at most, 10 cents difference in price between the two whenever I've seen them,) I'd say if you're looking for a good hit of chocolate with hazelnuts for a bit of added crunch and protein, you want to go for the Côte D'or.