Suppose the true model is $y=\beta_1x_1+\beta_2x_2+v$, so by the classical regression theory, we can estimate $\beta_1$ by $(x_1'M x_1)^{-1}x_1'My$, where $M=I-x_2(x_2'x_2)^{-1}x_2'$. And I can calculate the variable of $\hat{\beta_1}$ by $var=\sigma^2 (x_1'M x_1)^{-1}$.
However, suppose that I have estimated the model $y=b_1x_1+u$. So the variance of $\hat{b_1}$ is simply $\sigma^2(x_1'x_1)^{-1}$.
I am wondering how can I compare these two variances? Can I figure out which one is smaller?