"She likes his career."
Translation:Hun kan godt lide hans karriere.
There is no difference. It is not wrong using one or the other and one is not better than the other. Just 2 ways to say the same thing but kan godt lide is more precise. It adds a little something personal. Danes love adverbs and have a big collection of useless one they use constantly. You get used to it after some time.
But think of sit down, come over here etc. It is the same in all languages.