Is it better for Google ranking to host your blog, or let blog site?

Not sure your web site would get better ranking if blog service hosts it.

[JeffOstroff]

We are thinking of adding a blog to one of our sites.
But I am unsure whether we should try to host the blog ourselves under our own web site, then we can benefit in Google by having all the extra pages that grow out of adding blog entries to our blog.
Maybe there's a lot of technical fallout from that also?
The other choice is to use one of the blog service providers to host our blog on their service. But I don't see how that would help the ranking of our web site in Google if my content starts appearing on

myblog.BlogHosting Servicee.com,

instead of on my site at:

blog.mysite.com

Anyone have any suggestions?

[JeffOstroff]

I looked at Matt Cutt's blog, looks like he's hosting his own wordpress.

But still don't know if it's better to let the blog vendor host it. I know it's easier to manage that way, but the way I see it, your blog software vendor will be the one benefitting by the traffic and rank, not your web site.

Anyone got any opinions?

[eeek]

Host your own. Why let someone else make the money?