In the big picture, I don't think it will make a huge difference. (Keep in mind, I'm speaking as one who's employer runs multiple websites, including a free-standing blog.)
The way I see it:
You're still going to want to link between the blog posts and the rest of your site, whether the blog is integrated or freestanding. If a blog post brings in a visitor, you don't want to leave the visitor hanging at the end of the article. You want to make it clear to them what they should do next (for instance: sign up for your newsletter, shop for a product, sign up for a free trial, download a white paper, or whatever).
One advantage of having the blog integrated with your main website is that your internal site navigation will take up part of the slack for this linking. While you'll still want to include calls to action in individual blog posts (and elsewhere throughout your site, for that matter!) the site's own internal navigation / menu system may help draw blog visitors further in to the site as well.
Another advantage is that when people link to a blog post, that same internal site navigation will help the link benefit "flow" through your site to help additional pages. (But, if the blog is separate, simply making sure each page contains at least one link back to the main site can accomplish pretty much the same thing.)
There are advantages to running the blog as a separate entity, as well. A little separation may make it easier for the blog writers to adopt the slightly more casual, "breezy" tone that often works better on blogs than the more formal corporate language typical of primary sites. And having a standalone blog allows you to develop a distinct look and feel for the blog itself, rather than simply inheriting the look of the main corporate site. Both of which can be good things, but honestly don't mean squat when it comes to SEO.
And you were asking specifically about SEO benefit. My opinion: as long as you link from the blog to the main website (or -- assuming the blog is integrated into the main site -- from the blog pages to the other pages within the same website) I don't think it's going to make an enormous difference. Do whichever one works better for you from an administrative and/or design point of view.
Others may have a different perspective on this, though, so you may want to wait for additional answers before you decide.