You nailed it. Twitter’s existential strength is its Interest Graph — a competitive advantage relative to Facebook’s Social Graph.
However, Twitter’s shortfall is also its Interest Graph, because it’s so dependent on whom you Follow. In other words, by allowing you to unilaterally follow users (as opposed to bilaterally friend-ing people on FB), you manually curate whom you’re exposed to. While that creates a purer signal of relevant content for your interests, there’s still a lot of noise.
The upside to some of this noise is serendipity, but Twitter needs to keep working on generating purer signal to service our interests through this noise, because the ratio of noise to signal volume (and discovery to consumption time) is still too high.