Hello, Leo! They are nearly the same. "Aš mėgstu" lithuanians usualy use to express preferences in not live objects (such as food, activities, hobbies etc) and "Man patinka" you can also use when you are talking about a person or live object. Also, you need to use nominative case with "Man patinka" and accusative case with "aš mėgstu". For example, "Man patinka sportAS" and "Aš mėgstu sportĄ". Hope that I helped you!