At least in my area, journals aren't things you "browse" anymore, because the big journals have very disparate sub-fields represented in them, most of which I don't regularly keep up on. They're closer to repositories where papers get filed away. The sub-field I care about publishes regularly in 5-6 journals/conferences, and somewhat less regularly in another 15-20 or so, so what I really want is the non-existent Journal of the Stuff I Research, whose centroid is my own research. In reality, that journal is scattered across a bunch of other publications, but Mendeley makes some effort to reconstruct it for me.
Just following something super-broad like Science or Artificial Intelligence, though, isn't as useful to me, because the vast majority of papers just aren't going to be relevant to my research.