Caching Views: Query results Vs Rendered Output Can you think of an example when it would be beneficial to have the Query Results cache time be longer than the Rendered Output time? or vice versa?
First some explanations:

Caching your query results, means you store the results. So the next page load you don't have to perform your heavy time consuming SQL query again. 

Caching the rendered output means you cache the generated HTML output; the system does not have to render the page again.

It would make sense to have most of these exipire at the same time,  after all, if the data changes, you'd want to show the changes to the user.

The only situation I can think of to cache the query results longer than the SQL data, is in a situation where the template file changes very often. Your theme might for instace randomly change the color of each table row, or show the current time (provided via a theme variable and a preprocess function) on the display. You might want to keep this out of the cache to give the user the impression the data is current, while still being able to serve the page relatively fast.

Caching the rendered output longer than the query seems like a bad idea. You'd be performing the resource intensive SQL query for new data, yet discard the data directly because you choose to display the old data instead. So I'd recommend against doing that.