voltage gain and current gain in a common emitter
If we assume \$\beta = 200 \$ the voltage gain is: 
$$ A_v \approx - \frac{R_3}{\frac{R2 + r_\pi}{(\beta+1)}}\approx -8.7\; V/V$$ 

And you get the wrong result because you don't include R2 influence. 

Transistor gain alone is \$ - gm*R_O = 47.6mS * 4.3K \Omega = - 204 \; V/V \$ 

But this is true only if the base is connected directly to the input source. 

In your circuit we have \$R_2\$ in series with \$r_ \pi\$. 

Hence, we have the voltage divider

$$\frac{r_\pi}{R2+r_\pi} = \frac{8.4k\Omega}{8.4k\Omega + 100k \Omega} = 0.07749 $$ 

So, the overall voltage gain is 

$$Av = -204 * 0.07749 = - 15.8 \; V/V$$