Let the two circles be $S_1: x^2 + y^2 + 2x + 3y + 1 = 0$ and $S_2: x^2 + y^2 + 4x + 3y + 2 = 0$. The equation of the common chord (radical axis) is $S_1 - S_2 = 0$. $(x^2 + y^2 + 2x + 3y + 1) - (x^2 + y^2 + 4x + 3y + 2) = 0$ $-2x - 1 = 0 \Rightarrow 2x + 1 = 0 \Rightarrow x = -\frac{1}{2}$.

For circle $S_1$, the center $C_1 = (-1, -\frac{3}{2})$ and radius $r_1 = \sqrt{(-1)^2 + (-\frac{3}{2})^2 - 1} = \sqrt{1 + \frac{9}{4} - 1} = \sqrt{\frac{9}{4}} = \frac{3}{2}$. The distance $d$ from the center $C_1$ to the common chord $x = -\frac{1}{2}$ is $d = |-1 - (-\frac{1}{2})| = |-1 + \frac{1}{2}| = |-\frac{1}{2}| = \frac{1}{2}$.

The length of half the common chord, say $L/2$, can be found using the Pythagorean theorem: $(L/2)^2 = r_1^2 - d^2$. $L/2 = \sqrt{r_1^2 - d^2} = \sqrt{(\frac{3}{2})^2 - (\frac{1}{2})^2} = \sqrt{\frac{9}{4} - \frac{1}{4}} = \sqrt{\frac{8}{4}} = \sqrt{2}$. The total length of the common chord is $2 \times (L/2) = 2\sqrt{2}$.

Options B, C, and D provide incorrect lengths, as they do not result from the correct application of the distance and Pythagorean formulas.