We tend to avoid "~는 것을 좋아하다" in the first place since it's loooong. It's about efficiency.
What we hear most often: "저는 독서를 좋아해요"
As you can see, we usually transform "to do something" to a noun. (독서: reading books)
"즐겨" has an additional meaning/nuance of being an habit, actually done very often on a daily basis.
"저는 책을 읽는 것을(독서를) 좋아해요"
It means that you like reading books, and even put it to your schedule.
"저는 책을 즐겨 읽어요"
It in addition means that you actually read books very often, pretty much at every opportunity in your spare/niche time.