Use ND filters when there's too much light to get correct exposure at approximately 1/fps shutter speed. For example, shooting at 24fps, try to keep shutter at 1/50th, at 30fps, shutter around 1/60th. This is a rule of thumb, and there's some wiggle room and also there are reasons to break away from that guideline for specific special effects. You can still shoot auto, if you need to, and use an ND filter. For example, choose the ND filter that gets you even exposure in the general environment you're shooting in, with the desired shutter speed for the fps. Then, as you fly, let the auto exposure mode make the minor adjustments to shutter or ISO and you're at least within the ballpark.
Pet peeve: the Phantom doesn't have a shutter priority mode. If only you could set the shutter speed (better yet, an acceptable upper/lower speed) and let it float ISO up (with a ceiling) if needed, it'd be ideal. Strangely, I've seen it push ISO UP to 400, while at the same time cranking shutter UP.... makes no sense whatsoever one adds light (and noise) and the other lowers light (and affects motion) so they're fighting each other, so I avoid auto mode.
PL filters are a special case. They block a particular kind of light: reflected light, generally speaking. If you're shooting where there is a lot of reflection, you will see a difference. For example, around water, or in a sun-dappled forest where light is reflected off foliage. You will see a big difference using polarizer filters in those situations.
