The advantage of a tweetstorm is that readers can like/retweet individual paragraphs. This high-granularity feedback can be surprisingly useful data to the writer.
On the other hand, it encourages writers to make every individual paragraph as inflammatory as possible (I've never once read a quality newspaper article with "Let that sink in" in it), wilfully encourages paragraphs to be taken out of context, and means that 'readers' get a half-baked thought from the middle of an article dumped in their newstream. This is entirely not how media was meant to be consumed.