What is the difference between an 'Attachment display' and a 'Global: View area' put into header/footer of a view?
Background: View is a view,  a view can have many displays, such as page, feed, attachment, block.

With Attachment display, you can attached one display of a view to another display.   A good video demo can be found by Doug Vann (its a drupal 6 demo, that can relate to drupal 7).   

With Global: View area (Drupal 7 only)  you can add a view inside a view header or footer.  

This is no huge pro/con of doing it one way over another.    The only thing I can think of is templating a view and styling it. There will be different html tags and classes for you to style.