Basically both are OK, but they're used separately when confusion arises. 彼のお気に入りのバイクはこわれてしまった。Better, because 彼の好きなバイクはこわれてしまった。is a bit awkward. お気に入りのバイクのタイプは何ですか？ Confusing as your favourite type of motorbike or the type of your favourite bike. 好きなバイクのタイプは何ですか？ Asking your favourite type of motorbike. This would be preferred. So that depends on what you want to say. Just my guess but お気に入りのバイク might be better.