I have built both the Dodd Battery Buffer and the Pass B1 buffer running on batteries.  
I could not get the B1 quiet.  It picks up local EMI and gets into the signal path.  I have tried a few ways to shield it, but still noise pickup.
The Dodd is dead quiet in my system running off a 12V AGM battery.  Sounds great with the 6H30P-DR tube!