A little better compared to playing Arkanoid DS (where it was moving too fast like Hammy on caffeine - watch Over the Hedge and you'll get my drift), but this time, the Paddle Controller is too slow. You can see that minute movement is pretty jerky and this being Space Invaders, you'll find yourself needing to anticipate your moves sooner to avoid getting boxed in by enemy fire.
Forget about side-stepping shots at the last moment, the Paddle Controller is simply too slow. You are better off using the D-pad. Coincidentally, the D-pad is used as the fire button if you have the Paddle Controller connected instead, so there's no switching from Paddle to D-pad on the fly when it comes to movement.
One minor detail that I notice is unlike Arkanoid DS (or Mario Kart DS post-patch), you can't use the Paddle Controller while in Space Invaders Extreme's menu mode.
I think it's time to put the Paddle Controller back into its box. And say "Welcome back, D-pad!"