It's a bit of a weird comparison, as they're quite different in terms of use.
A better one would be the Sigma 17-70 F2.8-4 HSM OS C lens, which is a bit more expensive than the 17-50 F2.8 HSM OS lens, but still quite good with the added benefit of more range.
If I were choosing between the Sigma 17-70 and Nikon 16-80, I'd probably go for the Sigma just because of the price difference as I believe there isn't that much of a gap in terms of optical performance, unless I really needed that extra mm at the wide end and 10mm at the tele.
Otherwise the Sigma 17-50 HSM OS is a bargain regardless, but less of a 'walk around' lens than the other two.