Well, with regard to ordering, as said, I have no idea how people bear with pivotal's complete lack of any way to express dependencies. Those are at the heart of any project I've been involved with, as stuff naturally gets delayed and shuffled around all the time. I have yet to find a sensible way to get a comprehensive status-view of a given Goal (consisting of multiple stories) in pivotal.

Take for example this mantis ticket, esp. the "Relationships": http://www.mantisbt.org/bugs/view.php?id=11330

At a glance I can see what state this Goal is in, what the progress is, what it depends on, what it is blocked on (if anything) and who is involved.

With a few plugins mantis will also add fancy progressbars and time estimates. I think there's even a plugin to compute a velocity similar to pivotal, even though I've found that feature amazingly useless in pivotal so far. Perhaps it works better when your tasks are very uniform and your teammates are robots instead of humans. ;-)

As for the higher level ordering (enforcing an ordering on Goals), for that Mantis uses the Roadmap, which can ofcourse also be modified at any time as needed; http://www.mantisbt.org/bugs/roadmap_page.php

Note also that all those extra-fields that are enabled in that mantis installation (Platform, OS etc.) are optional and customizable. In my setups there's usually only one or two, which reduces the UI clutter.

Note also the concise "Issue history" at the bottom which I much prefer over the cumbersome, ajaxified, collapsing/jumping mess in pivotal.

Anyways, to each their own. Different people, different priorities ;-)