I don't... but purely hypothetically, if I imagine I had a lot of free time now and lots of articles planned to write, here are the arguments.
In favor of LW:
The infrastructure is ready. I don't need to develop or configure anything, just start typing. It will support text, pictures, TeX equations.
My articles are immediately delivered to a smart audience. I don't need to advertise, exchange links, or anything; just write. If at some moment I happen to have a writer's block, and don't write anything for months, when I overcome it and write another article, the audience is still there.
The infrastructure includes selecting best comments and spam removal. I don't have to worry about the comment section.
This all implies the same thing -- my time and energy could be spent 100% writing, 0% maintenance, promotion, fighting spam and crackpots, moderating flame wars, etc. This is also important because if I decide to take a break later, it's not like the spammers would take a break, too.
In favor of a personal blog:
In case of huge success, possibility of generating income by advertising or selling my own (hypothetical) products and services,
Freedom to write about topics that don't belong to LW. I could post kitten memes and/or political propaganda; start my own pseudo-rationality-based cult, sell homeopathics or quantum therapy.
Even in case of selling a serious product, I could censor the discussion and remove mentions of my competitors.
This all implies the same thing -- by publishing on LW, I accept some limitations of form and content. By publishing on my personal blog I retain complete freedom.
Not sure if LW allows JavaScript in articles. If yes, this is possibly a security hole. If no, my personal blog would allow me to add all kinds of animations and interactivity into my articles.
Why not both?
I could start posting on LW, just to see whether I have the ability to generate sufficient amounts of interesting texts. I can always move or copy them on my blog later.
To avoid becoming a part-time moderator, I could simply not allow discussion on my blog. The articles cross-posted to LW would have a discussion here, the remaining ones would have no discussion.
I've had my blog since before LW had a "nothing is off topic" section, and I've cross-posted almost everything I've written since LW2 came out, and everything I've written since the mods set up automatic cross posting for me. I set up a separate RSS feed so that I could exclude some things, but I haven't excluded anything yet.
I don't actually feel like nothing is off topic on personal blog posts, and since I currently at least click through to most of what gets posted to LW, I'm kind of glad that we don't get people posting daily pictures of their cat. (And if they did do that, I'm not really sure what voting on those posts would be meant to indicate. I'd feel bad downvoting that in a way that I don't feel bad downvoting incoherent ramblings.) So if I do exclude something in future, it may be because I feel like it's off topic regardless of what the LW team thinks.
(I'd previously intended not to cross post my posts about software. But I saw someone specifically say they wanted to see more about programming here, so I figured why not.)
to those it applies