You can use array_diff(). For example:
$current_files = get_current_files();
$post_files = $_POST['choose_files'];
$remove = array_diff($current_files, $post_files);
$add = array_diff($post_files, $current_files);
if (!empty($remove)) {
// remove these files from DB
}
if (!empty($add)) {
// add these files to DB
}