In both cases, a lot of it has to do with increased censorship. A large number of people left 4chan for 8chan after moot started engaging in fairly aggressive political censorship. Who knows what his motivation was - maybe an effort to appeal more to advertisers, maybe a change in beliefs about freedom of expression - either way, the effect was the same. There was a big exodus to other chan sites.
Twitter has a similar censorship problem; many of the twitter accounts I followed, which were mildly offensive but nothing compared to the worst of the site, were silently banned without justification. The only connection I can find between them is that they were political in a way Twitter didn't like. Unfortunately, twitter is too big for there to be an effective exodus, so the whole internet is just worse off.
Not all nostalgia is misplaced. The internet is unquestionably changing, and the trend seems to be that as a system becomes more popular, it becomes more hostile to viewpoints too far from its median. Reddit, twitter, Facebook, etc. have all been extremely ban-happy in recent years, moreso than ever before.