The Datafield Template is used to provide editors with easy access to portions of content without having to dig through a page to find where to edit it. Clicking on a Quick Edit Wrench will send you to a simple page asking for a fragment of content to put in that specific location. The Advanced Edit Wrench on the other hand, while it also contains a fragment of content for that specific location, is used to deal with fragments that aren't as simple. Advanced Edit Wrenches are usually used to either supply values for complex templates (which more than just being displayed actually get used by the wiki to generate the page, and could then break the page if done wrong) or are used to display a large portion of a wiki article and thus contains all the regular wiki formatting inside it.
Editors who want to stick to contributing content without much knowledge of wiki formatting may want to stick to exclusively only using the Quick Edit Wrench to make all changes.