in the mac environment you have many choices. here are a few that i've used for both. i'm sure someone else will either back me up or recommend something they've used and liked.
For diagraming I would recommend OmniGraffle by OmniGroup.
http://www.omnigroup.com/applications/omnigraffle/pro/
Although you're not looking for it it will import / export Visio files.
For project management you can check out
http://www.aecsoftware.com/products/...ult.asp?bhcp=1
or
http://www.sharedplan.com/
FastTrack (top one) will import/export MS Project, bottom one will import MS Project.