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Quite frankly I was suprised that many people argued there was no difference to Google. Let me put this question another way.
All other things being equal, doesn't a top level page have a higher importance than a lower level page? In other words, a home page of a site subtopic.mydomain.com would have more importance for the spider's perspective than a subpage or subdirectory of a site www.mydomain.com/subtopic or /subtopic.html - all other things being equal.
This would seem to conclude, on your major sub sections of your site, you are better off putting them on their own subdomains so they appear as a home page instead of a subpage of the same domain.
There's a big caveat here in that I keep saying all other things being equal. That's not reality. In reality, the main site www.mydomain.com probably has a better PR than subdomain.mydomain.com because most of the inbound links point to www.mydomain.com. Since Google sees the subdomain site as a separate site, it is not able to take advantage of the trickle down of the higher PR on the www.mydomain.com site. Therefore, there may be many instances where a subpage on a domain with a high PR will rank better than a home page on a subdomain site with a lower PR (again, all other things regarding the page's ranking being equal.) This is assuming though that Google truly treats subdomains as separate sites and does not transfer any PR from the root domain. This would make sense since some domains truly do have separate entities/companies utilizing subdomains of a main domain.
The other question is will Google penalize, reward, or do nothing if you do both even when the pages are identical.
It seems the best way to go is to make a signficantly difference version of the page, one for the subdomain and one for the subpage and see which one ranks better?