Try this:
while ( $query->have_posts() ) : $query->the_post();
if ( has_tag('tag-slug') )
{
get_template_part( 'content', 'tag-slug' );
}
else
{
get_template_part( 'content' );
}
endwhile;
You would then need to create content.php
and content-tag-slug.php
with the appropriate content.
You could also look into setting up Post Formats. A bit more work up front, but a nicer experience down the road.