G'Day Lurkin - I have a 36v BBS01 from Ewan Maxwell's emax-ebikes here is Aus and it is delivering current as follows.
9 levels of PAS, highest PAS assist is 10.5A - full throttle at all levels of PAS, highest full throttle amps is 17.5A. I have a CA V2.
This is the "350w" BBS01 controller that is a direct swap for the "250w" BBS01 controller and may in fact be an identical controller just programmed differently.
The bike is plenty quick enough with this setup for me and the lumpy bits around me - Strava keeps chucking me out of KOMs as the rides are flagged as being with a vehicle. Personally I think less than 100 bucks for a second controller, meaning you have a spare, is a better investment than swapping from a BBS01 to a BBS02 - which probably requires a 48v change too to fully maximise the benefit. Unless of course you have two bikes and are putting the BBS01 on that.
Are you looking for more torque or top speed or both? I can sit on the flat in the low 40 km/hs on PAS at the 10.5A assist level. The extra beans with the throttle gets about 10% more speed, though I'll sometimes use the throttle as a boost when climbing.
So, the BBS02 on my cycling routes would be of minimal additional benefit to me personally, and make the bike heavier - ymmv. I can recommend you give Ewan a call, he's a good guy and when I explained what I was looking for he recommended I go with the BBS01 over the BBS02. Couldn't be happier with the system I have.