11.B. Given the parabolas $C_{1}: y=-x^{2}-3 x+4$ and $C_{2}: y=x^{2}-3 x-4$ intersect at points $A$ and $B$, point $P$ is on parabola $C_{1}$ and lies between points $A$ and $B$; point $Q$ is on parabola $C_{2}$, also lying between points $A$ and $B$.
(1) Find the length of segment $A B$;
(2) When $P Q \parallel y$-axis, find the maximum length of $P Q$.
11. B. (1) Solve the system of equations $\left\{\begin{array}{l}y=-x^{2}-3 x+4, \\ y=x^{2}-3 x-4,\end{array}\right.$ to get
$$
\left\{\begin{array} { l } 
{ x _ { 1 } = - 2 , } \\
{ y _ { 1 } = 6 , }
\end{array} \left\{\begin{array}{l}
x_{2}=2, \\
y_{2}=-6 .
\end{array}\right.\right.
$$

Therefore, $A(-2,6)$ and $B(2,-6)$.
Thus, $A B=\sqrt{(2+2)^{2}+(-6-6)^{2}}=4 \sqrt{10}$.
(2) As shown in Figure 11, when
$P Q / / y$ axis, set
$$
\begin{array}{l}
P\left(t,-t^{2}-3 t+4\right), \\
Q\left(t, t^{2}-3 t-4\right) \\
(-2<t<2) .
\end{array}
$$

Then $P Q=2\left(4-t^{2}\right)$
$\leqslant 8$.
Equality holds if and only if $t=0$.

Therefore, the maximum length of $P Q$ is 8.