More of an opinion / discussion piece.
When passing a lot of data, either via ajax, or simply refreshing the
page and getting a lot of data back, is it better from a "amount of work
placed on the server" perspective to do a full page refresh or to do an
ajax refresh of parts of the page, data intensive or no? Thoughts?
Depends on how much data you are changing overall. If you've got a pretty bare bones page with a lot of content (by which I mean actual content, not side bars and stuff) and you're replacing the entire thing it doesn't matter which way you go.
Now, if your page has a really complicated sidebar that once loaded never changes, but takes a lot of time/resources to load the first time, and your content isn't that much, then maybe ajax is a better way to go.
Don't forget to consider web spiders though and the ability to bookmark that page, and folks for which ajax won't work, etc...
My personal take on it is... if by using ajax the user experience is much much better I'll use it. Otherwise it's not worth it.