I think this really depends on what type of music you're playing. I use a BD pillow and usually prefer a small hole in the resonant head. I want a fat, beefy punch rather than an extended "booooom" coming from my kick.You can control sound and avoid dampening using a thicker head. Most people tune their bass drums too tight and with heads that are too thin, then they stuff the drum full of bedding to choke its sound.
My drum is made of extremely dense solid wood, supposedly the worst kind for ringiness, but I control it well with thick heads. Pillows don't produce good sound so I don't want the sound of a pillow coming out of the drum.
I hate the way the kick feels w/o a little padding and a small hole in the reso head, too. I don't bury the beater at all, I just think the head response is too spastic w/o those things. I tune both sides very loose and the pillow helps it feel less "floppy".
I feel like ghost notes get lost a little with too much "boom", as well.
The kick is the only drum I dampen...the rest are as wide open as Kansas. If you tune well (I'm a much better tuner than I am a drummer) you shouldn't need anything.
I especially hate the sound of a heavily dampened snare. Some guys will go out of their way to make sure the snare only makes ONE sound, when it's capable of so much more. Snares that have no ring sound dull and uninteresting to me.