Hi!
I tried to use pretty permalink, but couldn't make it work. Looks like wordpress doesn't support this kind of links.
I'm not sure, whether it uses category.php or tag.php, but according to this article http://codex.wordpress.org/Template_Hierarchy you can delete category.php and tag.php, then wordpress will use archive.php for category + tag combination.
In archive.php you can use a condition like:
if ( is_tag() && is_category()) {
//do something only when category and tag were chosen
}