Visio was the best diagramming tool in 1999, it's still popular in the enterprise, biz types love it; omnigraffle is more for designers, engineers who use macs, different markets to be sure.
Visio is a piece of shit I will say.
Word obviously supports Microsoft automation stuff that's unique to its own ecosystem, but aside from that and index generation, Pages is actually ahead of Word. (Not "light years", but heck it's a word-processor.)
Don't like Ribbons? Double click one of the groups and they go away http://officeblogs.net/UI/sizepics/RibbonCollapsed.png
And I don't know how you can complain about that when Pages is full of horrible trays...
Papers: LaTeX or Word with a proper template (you actually have to know a lot about how to use Word for such things to be effective.)
Wedding invitations: Publisher
Everything else: Word.