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Canonicals can pass link juice (see Dr. Pete's comment here), but it's at Google's discretion. I've seen it go both ways. The best way is to only link the one version you've chosen as the canonical. I'm not familiar with Magento - is that something that you can change easily? I think it'd be worth the time you'd invest in making that change.

Yes correct the blog is site.com/blog and has high quality content with many high ranking pages and high quality score. I will clean it up and try to maintain it again as the blog has not been looked after for a while and can be a good source for extra traffic. Many thanks for all comments it really helps!