OK.

First thing: Subdomains are treated as sites in themselves, so a link can be considered to be inbound-only and relevant. With respect to a blog, it can help, particularly if the subdomain is built out of desirable keywords. It depends on the blog tool used as to how often it is indexed, once found by search engines.

Second thing: Offsite blogs (such as blogger.com) have the advantage of being separately indexed on a totally different IP block to say nothing of being a Google property. This is way cool. I have been able to achieve #1 ranks for certain keyword sets this way. The downside is that you need to abide by Google's (Blogger's) terms of service, and you may find out that something is disallowed halfway through a process that is working.

Third thing: Onsite dedicated blog pages have the advantage of being the sole destination for people interested in your blog offering. But, unless you are certain of the originality of your content, I wouldn't go there.

Fourth thing: I have found and iFrame embed to be a wonderful solution since people can find and read the blog within the site, but it counts as an inbound-only relevant link since iFrame-embedded content is not indexed as part of page content.

Here is an example:
Self-Promotion, Product Development, Digital Media & Internet Marketing New Earth Arts Blog