Hi! I was finally able to spend a few hours with both pedals. I'll do a review of the B3k first, and then I'll compare it to the Xotic BB. I must say that I have not a lot of experience with different OD/distortion pedals, and I'm not very good with tonal descriptions. I'll try my best anyway. Make whatever question you want. I play a Valenti jazz with Sadowsky pups in passive mode, thru a SVT-VR with the Ultra-High switch on (about +15dB @ 8kHz). The cabs are Mesa Boogie Powerhouse 4x10 and 1x15 with the tweeter attenuators at -2 dB. I always play overdrive and distortion with a pick. All this info is quite important.
First, the B3K is the lightest pedal I've ever handled. It seems empty, weighs nothing. But it sounds great, the vast majority of Youtube clips are very accurate of its tone. It is what I was looking for.
The pedal tends to emphasize the attack, making your tone very cutting and articulated. The attack switch in "boost" position will accent this even more. This is the main characteristic of the B3K. This is an inherent tonal feature, nearly impossible to dial out (I guess that's where the B7K could act). So if you are looking for that cutting, grinding, articulated-and-agressive-at-the-same-time tone, great. I do.
The range of drive/distortion is similar to a RAT, IMO. I don't like it past 12 o'clock, it sounds a bit fizzy to me. BUT, remember I play with the UltraBright switch of the SVT. So, the amount of gain available should offer you tones from low gain to distorted. I set the drive on the B3K (and on my RAT) at 10-11 o'clock.
The low end is perfectly preserved in Grunt "Fat" and "Raw" positions. That's not the case with the Grunt "Thin" position, but there may be players who would want to lose some low end in a given situation, so who knows

The Grunt "Fat" mode also seems to boost some low mids (250 Hz?), but I could be very wrong.
The best way I've found to resume the tone of the B3K is this bass clip of Faith No More:
Faith No More - Epic Isolated Bass Track - YouTube The pedal will tend to make your bass sound like this Billy Gould tone. Hopefully this is what you are looking for.