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What’s the difference between SUR and iterated SUR?

I know the latter iterates on the weighting matrix and coefficient vector either simultaneously or sequentially. That suggests to me that is should perform better than non-iterated SUR. And yet non-iterated SUR is the default option marked when you enter the estimation box. I've estimated a non-linear system with both methods and found one produces a certain parameter sig at 1% (SUR) and the other only at 20% (i-SUR). I was struck and confused by the result.

Also I've found that it doesn’t seem to matter much whether you iterate sequentially or simultaneously. Is one somehow better or more reliable than the other?

Thanks.

Iterated enforces consistency between the residuals that are used to estimate the covariance matrix and the covariance matrix used in estimation. One-step is asymptotically equivalent and faster, and the default of non-interation accords with the way that people estimated these models when introduced. I don't think that either is necessarily better and that fact that your significance levels differ so dramatically would give me pause.

The two options for estimation exist since in nonlinear settings, they may provide different answers (path dependence).