Blog on domain only, or fed from blogger site?

[Jake]

Duplicate content tends to get lower search ranking, I assume the first copy found is considered the originator, guess where Google looks first.

You might look into the Canonical tag that can be used to point to another site as well as an internal page as the master source that should get the link benefit. I kinda doubt they will think a feed could be the source but you could try Canonical on the blog.

Having the blog only on the same domain name as your main site is pretty likely to be a more powerful rank booster. If your blogger blog already used a custom name you could redirect backlinks to the main page.