We're going through this whole decision process right now.
We've been using Mantis for a couple of years but the email integration sucks! It's non-existent w/o a patch. What email support we have for being able to mail tickets into Mantis, I had to write and hack onto the code.
RT has fantastic email integration but unfortunately the interface looks like something from 1997. It needs to be updated to be more web2.0/AJAX-y.
RT also doesn't understand SCRUM, which while I think SCRUM is ridiculously stupid, managers love it. Management has seen JIRA and they really like that but I don't know/haven't tested JIRA's email integration to see if it works end-to-end.