[zirobi]

It's not a matter of one being objectively better than the other but which suits your needs.

The basic distinction, from a purely SEO perspective, is that blog.domain.com will be treated as its own entity whereas domain.com/blog will be treated as part of the main domain.com entity.

The question you have to ask yourself is whether you want to bolster the "value" of your main domain or if you want your blog to be an asset in its own right.

There is no right or wrong answer — there is simply what's best for your situation.

[michaelbuckbee]

Objectively better for SEO - and in particular if this isn’t a personal blog, but say a marketing site for your SAAS and then an accompanying blog. Having them in separate domains with very similar content hurts you

This has been fairly well beaten into the ground at this point.

[toddmorey]

I’d say objectively safer. Google is getting better at reconciling content split across subdomains as coming from a common source. Some Google experts have called it pretty much a solved problem, but I don’t think the data plays that out just yet. I do believe there will soon be a time that subdomain vs subfolder won’t matter for SEO. Just not quite there yet.