The Underwood has more output and is in many ways a better pickup. What the BB clamp has over it is the lightness and smaller contact points which interfere with the acoustic sound the least of any PU I've found that isn't invasive. I used to use a volume pedal with the amp off most of the time, now I use a kill switch.
The Underwood significantly mutes the acoustic sound.
My comment was in regards to the amplified sound. I never noticed any significant acoustic degradation from the mass of the pickup, but I believe there is some. I plugged in almost 100% of the time, so it was none issue.