GitHub actually straddles the line a little bit. You'll note that when browsing around through folders in a repo on GitHub that you get the faux loading indicator along the top, and then it shows the contents you're navigating to. Same with switching between code and issues, for example. But switch to a different repo and you get a full page refresh.

For my company's product, we're much more on the side of a traditional server-side app, because users will send off a batch of information (their customers to open a line of communication with), and then wait for the responses to roll in. But the dashboard page where we show responses is a partial-SPA, similar to GitHub: new responses are loaded asynchronously, and you will soon be able to switch to different views of the data without a reload. It's a good balance for our application.

I realize it's not answering your question about how to measure it, but hopefully it provides some anecdotes.