There is a slight difference in meaning; att se ut som carries more weight and implies a close resemblance between two people, while att likna implies a more vague resemblance. Han liknar sin mor is closer to saying He is similar to his mother or He has his mother's looks.
There's another expression which I think belongs to the southern US: "He favored his mother." I think that in most places it means he was nicer to her, but here in Tennessee, at least colloquially, it means he looked like her. (Don't get me started on "y'all.")
I'd never heard that meaning of "favored" (I'm British). I'd say someone "took after" his mother, though without context that probably implies temperament more than looks.
"He resembled this mother" was accepted, and to me this is a clearer translation.
Han ser ut som hans mamma gjorde.
Very literal translation in this case. :)
Is "He was similar to his mother" totally incorrect? In Swedish lessons I am better at Swedish than I am in English :D I understand the Swedish phrases but problems occur when they have to be translated to English, word by word. But getting better and better everyday!