Can someone tell me if either of these two methods has an advantage over the other and why?
$mydir = ABSPATH.'/wp-content/themes/mytheme/images';
$mydir = dirname(__FILE__).'/images';
They can both be used to obtain and absolute path to the images directory of "mytheme" regardless of structure of whether wordpress is installed on the root directory or in a subdirectory off the root. In both cases, they are being called from the functions.php file which is located under the "mytheme" folder.
I would personally prefer dirname() as it is always guaranteed to give me the correct result, while the ABSPATH method relies on a fixed theme path and theme name that can both change.
By the way, you can use __DIR__ instead of dirname(__FILE__).
For my own projects I would choose dirname(__FILE__), also there is a new constant in PHP:
__DIR__ === dirname(__FILE__)
ABSPATH is defined variable -> define("ABSPATH",__FILE__);
if i directly use magic constant __FILE__ .it will produce same result.
In CMS ABSPATH and framework use BASEPATH is used to get root information in the form of defined variable . In the end with the help of both we get same accurate result.