I think wider tires provide comfort, lessen the chances of breaking spokes (of which I'm paranoid after bad experiences), and make it easier to ride on occasional dirt roads. They also add a bit of weight and a bit of rolling resistance, though I find that pretty negligible when I'm carrying a big load.

I used Armadillo 700X28s on several tours. They worked fine. I used Schwalbe 700X32s on my most recent tour. I liked them better. On my next tour I'm thinking about even wider tires, because there's a long section on dirt roads.