Elise Bauer has put together a very interesting look into the US weblog tools market. Masahiko Satoh has taken similar data for the Japan market from blogfan.org and has made a corresponding map for Japan.
It's interesting to compare the two maps. It seems that in the US, the race is between Blogger and TypePad, with LiveJournal still a contender. None of the other services/platforms are even in the same race.
In Japan, however, it's much less clear who the leader is. That is probably due to the immaturity of the market, more than anything else. Blogging didn't really hit the public radar screen in Japan until 2004. Now there's upwards of 30 different services.
MasahikoSatoh.com: ブログASPサービスマーケットシェアデータ
elise.com: On the Job: Weblog Tools Market - Update February 2005

Why did you say that that it was between Blogger and TypePad (as opposed to Blogger and LiveJournal)?
Is it because of the disparity in growth-rates?
Dev, in the US stats from Elise, the two fastest-growing services are Blogger and TypePad, which is why I cited them. LiveJournal is growing, but not nearly as quickly.
Just to clarify, I wasn't trying to be argumentative about the choice, I was just curious as to the motivation for the choice.
If anything, the free LiveJournal version might be less of a competitor compared to the Paid tools/hosts, as many users have dead blogs hosted there, as well as significant number having multiple blogs, and then the rss-feed style regurgitate journals. That's all guesswork on my part though, given that I didn't find mention of these in Elise's writeup, and her collected raw data didn't seem to be available.
The reason I think deadblogs, multi-blogs, and rss-blogs might be disproportionately distributed is
(a) The varying solutions seem to attract different people (cooking/food being more popular on TypePad as she mentions) and,
(b) The statistics which one blogger accrued about how switching app's changed the length & frequency of his posts (Sorry, I don't remember the guy's link. I think it was on/through BoingBoing, or Waxy, but couldn't Google it up)
Here's the (b) link: http://www.plasticbag.org/archives/2004/11/five_years_of_plasticbagorg_the_visualisations.shtml
Apparrently, he switched from Blogger to MT, and his post frequency dropped, while his post length increased. Which is not to say there's a direct correlation to deadblogs etc. Just that tools can greatly effect usage patterns, and may lead to other skewness in distributions.
I don't have the access to the stats you guys have but my personal impression is this "blog" BS is really an American centric "we were first" kind of dirty American kind of thing.
What's a Blog? the only definition that actually fits is a page where info is presented newest to oldest generally dated.
In that case, Japan has LONG BEEN AHEAD OF THE WEST. Japan's personal websites of which there are zillions, almost everyone of them has a nikki page (or diary) in the form of a blog. These have been ubiquitous since I first came to Japan 8 years ago. Every personal Japanese webpage I've been to starts with a menu, one of the options on that menu is nearly always a nikki page, some of have an update page (history of updating). Most of them are manually updated but they all follow the format of a blog.
So cut the bragging. The west was second when it comes to "blogs".
I agree with Gregg to a point- the diary/nikki culture is an old and storied tradition in Japan. However, weblogs, as we see them today, can be argued to be a US-driven phenomenon. It's all about how one defines "weblog."