Like a bunch of folks out here, I've used the BP100 for over 10 years. That's on my big carved 7/8 used mainly for jazz. Quieter settings but some where I've had enough volume to get feedback. This is with the Fishman preamp. I've also recently started using a K&K pickup/preamp on my Englehardt Swingmaster for arguably really loud settings. Also gives me feedback at times. I've tried things raging from eq knob twiddling to taping the F holes with varied success. Some of these ideas came from other TB threads over the years.
IMHO, I get feedback from either set depending more on how the stage is set up. Invariably having my amp too directly and too close behind the bass, location and angle if my monitor, whether I'm in front of the mains or not, and even where other instruments are located. Heck - I've have my bass resonate fundamentals along with a guitarists' tuning based on whether sound is striking the back of my bass right.
If I'm playing with any amount of volume, I make sure that I'm a) well behind the mains, b) well in front of and at an angle away from my amp and c) keep my monitor at an angle (I.e. Pointed at the side of my bass rather that straight on at the table).
Just two cents based on my own experiences trying to sort this out. BTW - I now rarely get feedback and when I do a couple of minor physical changes makes the difference.
Also, no comment on the actual tone of the BP100. That's more elusive than sorting out feedback ;-)