I used to have a negative opinion about BB bullets..but have changed it since I have a few moulds on my Master Caster that deliver them.They are as accurate as flat base and I say this based on more than one caliber and more than one configuration.
This being said,bullet hardness is being given way too much importance in the fact that a bullet will or won't lead.Diameter of bullet vs diameter of chambers is far more important;but that has been said before and will again be written about.

What works for me and in many .38Spl or .357 Mag is as follows:
target load:148 WC BB H&G 50 on top of 2.6gr 700X(or 2.8 Bullseye or 2.7 Red Dot,Promo).
Soft Load:Lee Mould 125gr(comes out at 132gr)on top of 3.5gr Promo(804fps chronoed in a 6''bbl).
regular .38Spl:154gr SWC(NEI mould)propelled by 3.8gr Titegroup(899 fps chronoed from a 6'' bbl)
38 +P:same 154 Swc with 6.0 gr PowerPistol.Didn't chrono it yet but heads turn toward me on the firing line when I shoot these.PowerPistol is known to be noisy.I shoot these from a 4'' model 13.
All these loads will perform well;I shoot them handheld no rest and all will stay in 4'' at 25 when I'm having a good day(which is not often enough for my taste!).