I think the logic is that instead of everything going via a handful of servers at the big companies, it goes through many more thousands of individual PCs but of course, that depends on the technology used. Torrents should be faster but only if lots of people seed and don't simply download and disconnect.
It depends what's meant by "distributed". A content-addressable network could very well be faster because of the pervasive caching and it's immune to (D)DoS attacks. Things that aren't accessed frequently by a lot of people would be much slower.