I would say they are both grammatically correct. But the example sentences are a bit funny since no one would enjoy burping :-) People are more likely to say 저는 크게 트림하기를 잘해요 (I often burp a big one). Or 저는 큰 트림을 잘해요 (I often have a big burp) might be even better. 잘해요 here means "do often out of habit" (버릇으로 자주하다) whether you like it or not. For 좋아해요 we can think of a sentence like: 저는 늦게까지 자기를 좋아해요 ("I like to sleep late"). 저는 잠을 늦게까지 자기를 좋아해요. 저는 늦잠 자기를 좋아해요 (most natural).