Can someone enlighten me as to what is the difference/advantage of Publish vs. Export presets?
That's exactly the question I had before trying them out. The main difference is that it takes care of managing your site or Flickr account. You can set all your photos tagged "Flickr" * to be Published to Flickr. Then when you click on Publish it will send them automatically to Flickr, applying the Title and Caption field (if set). Then the magic part: if you make any changes to the photo or its metadata, and click on Publish again, it will update that photo for you on Flickr.
LR will also notice when you add a new photo with Flickr tag, or make any changes to existing photos, and mark them as "new photos to publish" or "modified photos to republish," and these will be done in a batch when you click on Publish.
So there's no more need to figure out which photos you have changed, when you last updated your Flickr/website, or play with messy presets, it's all done automatically by LR. I thought it was easy just to use my export reset to send all new photos to my site, but it's much easier just to tag them with "site" and click on Publish. It'll also republish them with one click if I ever choose to go for bigger photos (ie. when people's monitors start being more than 700 or so pixels high), or make any other changes to export settings, such as watermark, or make global changes to the photos.
* you can set this to any keyword, of course, or any other filters that can be set with smart collections. For example, I have set the photos going to my website as "keyword has [country] in it," "keyword starts with Harri" and "Copy Name is not thumbnail" - this way it groups all my photos from the Netherlands in one folder, Finland in another, etc., includes only photos which I have tagged as going to my site, and excludes square thumbnails which I have in my collection as virtual copies.