It depends on:
- Where the site's backlinks are pointed and
- How the site's internal links are structured
If the subdomain is basically completely isolated from the root domain, and the root domain is where most of the site's authority backlinks are pointed, then the subdomain would be weaker.
If the subdomain is getting more and/or better backlinks than the root domain, then the subdomain's links would generally be stronger (although it's generally much more common for the root domain to have more backlinks/authority).
Anyway, all of the text above is mostly an interesting sidenote, because you're probably asking about web 2.0s (e.g., somesite.wordpress.com), in which case the root domain would be like eight million times stronger, since the individual subdomains are designed to effectively be completely new, isolated, and separate domains (i.e., they're not getting power from the root domain, because the root domain isn't linking to them).