Testing if coefficients are statistically significantly different across models I will be building two zero-inflated negative binomial (ZINB) regression models, where each model is aiming to predict different disease count outcomes based on the exact same independent variables and data. For example:
$$Y_A =\beta_1^A X_1 + \beta_2^A X_2 + \beta_i^A X_i... + \beta_n^A X_n  \tag*{Eq.(A)}$$
$$Y_B = \beta_1^B X_1 + \beta_2^B X_2 + \beta_i^B X_i... + \beta_n^B X_n \tag*{Eq.(B)}$$
What would be the appropriate method to test if the $\beta$ coefficients are statistically significantly across models when the data from the independent variables are the same across the models? Such that:
$$H_0: \beta_1^A ~\text{in Eq.(A)} = \beta_1^B ~\text{in Eq.(B)} \\
H_A: \beta_1^A ~\text{in Eq.(A)} \ne \beta_1^B ~\text{in Eq.(B)}$$ 
I have investigated the use of Seemingly-Unrelated Regression (SUR) methods, but I am unsure if there is relevant literature to warrant their use in the form of a ZINB model. Is there another more simple means of testing if these $\beta$ coefficients are statistically significantly different from each other?
 A: So if you have something like:  
Scenario 1:
Data =
\begin{bmatrix}
    y_{1}       & b_{1} & b_{2} & \dots & b_{n} \\
      \vdots & \vdots & \vdots & \ddots & \vdots \\
    y_{1_k}       & b_{1_k} & b_{2_k} & \dots & b_{n_k}
\end{bmatrix}
model 1:  Y ~ B1 + B2 + . . . Bn  
AND
Scenario 2:
Data =
\begin{bmatrix}
    y_{1}       & b_{1} & b_{2} & \dots & b_{n} \\
      \vdots & \vdots & \vdots & \ddots & \vdots \\
    y_{1_j}       & b_{1_j} & b_{2_j} & \dots & b_{n_j}
\end{bmatrix}
model 1:  Y ~ B1 + B2 + . . . Bn  
Why not stack both data sets and add a dummy variable (G below) to denote each group? Where G = 'one' is group 1 and G = 'two' is group 2.
Combined scenario:
Data =
\begin{bmatrix}
    y_{1}       & b_{1} & b_{2} & \dots & b_{n} & G\\
      \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
    y_{1_{k+j}}     & b_{1_{k+j}} & b_{2_{k+j}} & \dots & b_{n_{k+j}} & G_{k+j}
\end{bmatrix}
Now your model can test the importance of the group variable.  
model 3: Y ~ B1 + B2 + . . . Bn + G + B1:G + B2:G + . . . Bn:G
You could also have interaction terms like B1:G in the model to test the importance of the interaction on that particular beta.
