The inequality is $\(441<x^2 \leq 1089\)$.
Since $x$ is an integer, we need to find the square roots of the boundary numbers.

$$
\(\begin{aligned}
& \sqrt{441}=21 \\
& \sqrt{1089}=33
\end{aligned}\)
$$


So, the inequality can be rewritten in terms terms of $x$ :

$$
\(21<|x| \leq 33\)
$$


This means $x$ can be positive or negative.
Case 1: $x$ is a positive integer.
If $x$ is positive, then $|x|=x$.
So, $\(21<x \leq 33\)$.
The possible integer values for $x$ are $\(22,23,24, \ldots, 33\)$.
Case 2: $x$ is a negative integer.
If $x$ is negative, then $\(|x|=-x\)$.
So, $\(21<-x \leq 33\)$.
Multiply the inequality by -1 and reverse the inequality signs:

$$
\(-33 \leq x<-21\)
$$


The possible integer values for $x$ are $\(-33,-32, \ldots,-22\)$.
Quantity A: Sum of all possible values of $x$

$$
\(\begin{aligned}
& \text { Sum }=(22+23+\cdots+33)+(-33+(-32)+\cdots+(-22)) \\
& \text { Sum }=(22+23+\cdots+33)-(33+32+\cdots+22)
\end{aligned}\)
$$


Notice that for every positive integer $k$ in the range $[22,33]$, there is a corresponding negative integer $-k$ in the range $[-33,-22]$.
When we sum these values, each positive value will cancel out its corresponding negative value:

$$
\(\begin{aligned}
& 22+(-22)=0 \\
& 23+(-23)=0 \\
& \ldots \\
& 33+(-33)=0
\end{aligned}\)
$$


Therefore, the sum of all possible values of $x$ is 0 .
Quantity B: 330
Comparison:
Quantity A $=0$
Quantity B $=330$
Since $\(0<330\)$, Quantity B is greater than Quantity A .
The final answer is Quantity B is greater.