Why should I use a subdomain structure over a directory structure?

The only time I would use a subdomain is if the site is truly a "different site". Take for example my business site I have the following setup.

http://www.iowacomputergurus.com - Business site

http://productsupport.iowacomputergurus.com - Bug Report Site

http://customersupport.iowacomputergurus.com - Customer Helpdesk site

Using this structure all of the business stuff, including the blog is on the one site, but the stuff that is truly different, the various support sites are offloaded to sub domains so that they are separate.

In my opinion, if you REALLY want to use blog.mysite.com say for ease of remembering, setup a 301 redirect that takes users to http://www.mysite.com/blog or something similar.

If you DO use subdomains, depending on the sophistication of your target audience, be prepared for users to add www. in front of the host name automatically (www.blog.example.com). Setting DNS up to support this is something that I've never taken the time to figure out; it's possible but takes more effort than just adding another CNAME.

The usual recommendation we hear from SEO consultants is that you should really only use a sub-domain for short-lived "micro-site" type content, and all long-term content should live on the main site.

As others have pointed out, you lose some of the "authority" (and therefore Page Rank, etc.) of the main site when you go out to a sub-domain because they are treated as separate sites - you've clearly decided that you don't want the content on the "main" site, therefore it is less relevant.