Mvregress and choice of the estimation algorithm

I am performing a multivariate regression analysis using mvregress:

[beta,Sigma] = mvregress(X,Y,'algorithm','cwls');

However, I noticed that, although the estimates are identical, the standard errors completely change if I use the cwls algorithm as opposed to the mvn one. In particular, with cwls, almost all coefficient appear as significant, while, using mvn, almost none of them is.

There are no missing responses in my data, so the default would be mvn.

Can a simple algorithm choice be so influential on the result? Is there a way I can choose wisely between the two?