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 ;-)
IMO one of the great strengths of pivotal is that there is a single view of the project. While tools such as mantisbt allow you to track lots of information (such as severity and interdependency) I'm not actually interested in this information beyond using it to decide what order work should be done. Pivotal forces you to resolve these factors into an ordering and in doing so provides a much simpler/clearer view of a project.
You could argue that not having this extra information makes reprioritisation harder. In practice I've found that this extra information is often subjective or temporary e.g. how severe an issue is/we really need this feature! I've always found that tracking these opinions is pointless as they change with such frequency that the tool is out of date anyway (ever hear arguments starting with "but you said it was severe two weeks ago"). In the end my experience is that people always know what the important issues are when prioritising, they don't need to keep them in a tool. They also appreciate a simple view of a project which I think pivotal does very well.