Some of you might find this video interesting.
They think the stock BD2 is completely useless, buried in the mix as soon as you step on it, at 9V but find it useful as a fuzz at 4V, and sound good as a drive pedal at 18V.
Both is best. When I played in bar bands, I always considered a Tubescreamer to be a security blanket to make sure that my leads could be heard (without being too loud) above the other guitar and keys. I didn’t use it a lot (I mostly relied on volume knob manipulation to boost volume when needed) but when I needed it it always came through. Blues Driver cannot do the same thing, but I love that pedal also and I think it has more cut than many other “transparent” overdrive pedals. Like many, I mostly use the BD as a dirty boost with the gain knob somewhere between 9 and 10 with my Tele (higher if using a Strat)
I use my TS with the gain almost all the way down and the volume all the way up. Then use it as a boost before my OCD to gain it up and get more saturation out of the OCD. This means I can bring the gain down on the OCD and get more tones (3) out of 2 pedals.. The TS is very low gain, mostly clean boost with mid hump to cut, the OCD is medium gain/crunchy, then I can boost the OCD with the TS to get full cutting distortion with both on. But the BD is a sweet pedal also.