I own a BC-1 and a B3k. Both of them have their own sound baked in for sure.
I find the BC-1 to have big lows and be a bit sharper up top, useful if you want that harshness. The clean channel is always on, so you'll always have the voicing of this pedal in your tone, and the drive is quite growly too. I wasn't a big fan at first but it does really growl through in the mix. Theres adjustable mid frequency selections too to change the flavour a little bit to what you want, though the boost footswitch just sounds horrible and buzzy.
I actually find the drive on the b3k to be a bit smooth and scooped, though this can probably be helped with the EQ on the b7k. This pedal is not transparent in the slightest, even with the blend up, so it depends if you like that inherent voicing or not. I really like the sound of the drive at low gain as it becomes a bit lifeless and fuzzy when you crank it more, but ive always had problems with trying to get unity gain with any setting on this pedal.
It's hard to say which one would be best for what you want. The BC-1 is more transparent with better mids and growl, the B7k probably sounds chunkier in the mix with a more natural low drive.