Thanks guys for your great feedback, it's very reguarding to read your comments, and it nice to show in some way, why there are many of us that prefer the single H.
The thing on the headstock as oli@bass said, is a Fat Finger. Being the headstock the less dense part of the neck, when you play some notes it vibrates in a very imperceptible way, producing that those notes have less sustain and volume than others. When you put a Fat Finger is like adding mass to the headstock, making less suceptible to vibrate.
In MusicMan basses this almost not happend, they have a really great tone balance. But when I add a Fat Finger I feel a little increase on lows, a more round tone, specially on high notes, and I like that. I also use a D-tuner, this heavier tuner machine has the secondary effect of adding an extra mass to the headstock. Fat finger + D-Tuner= No possible dead spots on the fingerboard