I currently have my app's marketing/external website on the root level, e.g. http://example.com

My web app itself is hosted at: http://app.example.com

What's the best strategy to set-up Google Analytics tracking for both of them? Should I create a separate web property? Also, what's the difference between creating a new web property and a new profile?

UPDATE: I would want to be able to track conversion from a page on the root domain to a sign-up page on the app sub-domain.