Tiki does everything you describe as native features with one exception: Gantt charts
For Gantt charts, there is unofficial code and we hope that someday, someone (maybe your group?) will volunteer to make it official code in Tiki: http://dev.tiki.org/TrackerToGanttChart
The best for you is to take the time to test both applications and pick the best for your current and planned needs.
If there are features which you feel are missing in Tiki, please do http://dev.tiki.org/Add+to+the+Wishlist
If you do pick Tiki, know that it's a community project and you are warmly invited to contribute your fixes and enhancements. Please see: Model.