If you put it on a subdomain, it is considered a completely different site. In this case, just like if it was on a different domain, you theoretically get some benefit from back-links to your primary domain. Putting the blog on your personal domain allows you to blog about things not related to the business. This gives you a bit more opportunity to write interesting articles that aren't overly self-serving. Assuming you can find an audience, you'll get rewarded with traffic to your startup's domain.
Of course, you could always have two blogs, one for personal, sometimes talking about the startup and one for the startup. Probably not worth it unless you really have enough content for both sites. An added benefit of using your personal blog to talk about the business is that if you sell it, you don't lose all of your content.