I also have two tanks: one high tech with co2 , the other one is low tech with no co2 .
The high tech always have bba , but weekly spot dosing of excel keeps it in check.
The plants in my low tech came from my high tech , so I was sure I was going to have same problem , to my surprise the BBA in my low tech didn't grow till the filter get clogged up while I was away. Once filter was cleaned , bba gave up , till I overstocked the tank. I then invested in TDS meter and started topping the tank off with RO water instead of regular tap water . TDS went down from 220+ to 150 and no more BBA .
I really think cleanliness of the water combined with stable parameters of the water is the key for BBA free tank.