If you use do_sortcode or you add the shortcode to the normal content area they are parsed the same. ACF 4 does not use the standard WP editor for its WYSIWYG fields, but it does it just calls do_shortcode, basically it just applies the same filters that WP does to the content in the standard editor. As far as I know there’s noting in ACF that would cause the standard WP gallery shortcode to function incorrectly.
I just testing on a site using ACF 4, adding a gallery to both the standard WP editor and to an ACF WYSIWYG field. I added different images to each and reordered them in both. For both galleries the images appear I selected appeared in the order that I set them.
The only thing that I can come up with is that you have something else on the site interfering with the operation of the WP gallery shortcode. What other plugins are you running? Try deactivating them. What theme are you using? It could be something in the theme.
