A lot of folks are calling this a better alternative to "the existing solutions" for Torrenting pirated content, because by replacing a website that can be shut down with a blockchain as the torrent index/repository, it is considerably more robust, but I want to be clear that this was not our actual goal - the purpose behind Alexandria is to use the P2P technology that piracy sites rely on for free wide distribution to enable artists to be in direct control of their works and how they are distributed and monetized. We're of course aware that pirates will find the platform to be an attractive solution to their biggest problems, and since there's no way we could prevent them from doing so without creating central points of failure w/in the system, we're "ok" with it, but we are taking steps to prevent those pirated works from actually showing up for end users in the Alexandria browser. As Joey (metacoin) pointed out, this will use a filter system that users can opt out of, because otherwise it would be a pretty dramatic example of 3rd party censorship, but we think it strikes a strong balance of making the core technology available in a really supportive way to the average end user while preventing it from being blatantly abused by piracy rings.

So, to more simply answer your question, the actual "existing solutions" this is attempting to better would be YouTube, Spotify, Soundcloud or iTunes, not thepiratebay or PopcornTime, and we think it offers many significant advantages over them (namely that it offers matching feature sets to those platforms, is uncensorable, has incredibly low distribution costs and lets artists monetize their works directly without any expensive middle-men).

Devon