It's a matter of building a relationship with a particular user vs an opportunity to advertise to many.
Liking a facebook page effectively 'subscribes' them to your content. This means far better retention than simply bookmarking, and poses less barriers to existing FB users than adding your feed to an RSS reader or email list. But it's a relationship, and users typically resist this if there's any reason not to trust your service or organization (i.e. it's commercial). A key question to ask yourself is: is it clear to users that my future content will continue to have value? If you write content on a narrow range of topics, and confront themes across multiple posts, perhaps so.
Liking an article shares it. This makes an item appear in the users' friends' news feeds, with the article's headline, image and perhaps a copy snippet. This is a great way to gain exposure, especially when a title or headline is particularly evocative (or even downright controversial). But the effect is transient. Still, this is acceptable if your content isn't going to regularly help a single user.
Ultimately, which sorts of exposure you want depends on your context and your strategy. Some services might not gain much from long-term relationships; others need it to thrive and persist. Those are big questions about product strategy, and only you can answer them.