I'm in the same boat with you (waiting for the funding correspondence from Duke). If I had to hazard a guess, I'd say that the reason we haven't received anything further yet is probably the same reason why Duke hasn't sent out all of its acceptances/waitlists. The funding letter (and hopefully information about accepted students weekend, etc.) is supposed to come from the department itself, whereas decisions thus far have been officially from the grad school. The department may still be making decisions--I'm almost certain that they are--and I can see them waiting to send the funding notices until they have their lineup of first choices settled. I'm also pretty sure that Duke fully funds all of its PhD students...anyone want to correct me there?
As for competitive offers, obviously you should look for a tuition waver, but that should be paired with a stipend that will allow you to live comfortably (everything you need, plus maybe a little wiggle room for things you want--any other opinions on this?) in the area. Calculate cost of living. $20,000 will be a much different sum in Palo Alto, CA than in Durham, NC, and you should evaluate offers accordingly. Consider what you'll spend for transportation to and from school a few times a year if you plan on going home for holidays. And are you being offered any money for summers? Travel? Research? Is this money coming to you in fellowship form or assistantship form? If your money is dependent upon you TAing, realize that it's going to cut into the time you can spend on your work, which could affect your time to degree. However, if it's all fellowship, are there opportunities for you to teach if you want to? Because the job market being brutal like it is, you're going to need teaching experience to be competitive outside of R1 schools.
There's also implicit department money when it comes to traveling to conferences, etc. that, while not part of your official funding, will affect whether or not part of your stipend goes toward you doing the things you need to do to get ahead in the market.
Would definitely love to hear everyone else's thoughts on this, though. It's an important question.