using the same model but different way to estimate? not sure if it's proper, you have two coefficient matrices (B1 and B2) and two variance matrices for the coefficients (V1 and V2), so use

(B1-B2)'*(B1-B2)/(V1+V2)

as a chi-square test with df = the dimension of V1?

respond to my answer: there can be problem, since the same sample or data is used to fit the same model, there are some covariance between B1 and B2, I don't know how to capture the covariance, if we know the covariance, we can use (B1-B2)'*(B1-B2)/(V1+V2+COV) as a chi-square test with unknown df (because of covariance).  Not sure if there is an easy way out.

Thank you.
It becomes much clear for me.

no problem.  one way is to us (B1-B2)'*(B1-B2)/(V1+V2) as an approximate, another way is to estimate the covariance and the df of the chi-square (maybe using bootstrap?).