I've had this blog for going on two and a half years now, and it's interesting to see how writing posts has influenced my "other" writing.
There is the obvious difference in interface. When I add citations to a paper, I almost wish I had a tool that could highlight text and add a clickable link to a reference (the emacs extension RefTeX is great, though: it makes adding citations, references and labels blindingly easy).
I structure sentences differently as well. Links in blogs are added en passant, without interrupting the text. Citations in papers have to be worked into the sentence structure carefully (that is, if you believe the maxim that a citation is not a noun). This causes no end of confusion when I write sentences in a paper; I often have to rephrase the sentence to conform to "normal" citation format. I will add though that the parenthetical style of mentioning citations makes sense with written documents, but with online hyperlinked PDF documents I would actually prefer blog-style linking. But then again, we still have paper proceedings, so there's a long way to go for that...
It's natural that a blog post is more chatty and personal, and a paper is more formal. But writing a blog has encouraged me to be less stuffy and more breezy in parts of a paper that merit it (introductions, discussion, etc). This can only be a good thing; as the famous war cry goes, 'Eschew obfuscation' !
Writing a blog also shakes out some of the ghastlier linguistic tics that infect my writing. It's actually shocking how many there are, and how easily they evade detection.
I wouldn't recommend writing a blog solely as a way of improving (or expanding) your writing skills. But it does have benefits beyond being a soapbox for one's bloviations.