I have both and BA is much easier to reach and retain status. I only use my QFF account to credit domestic or short haul QF flights to (because BA earning rates for avios and status are woeful since the end of the JSA). However if I flew QF long haul in premium classes, I'd credit it to BA unless I was looking to spend QFF on an upgrade.
BA is much more generous in status credits with other OneWorld carriers compared to QF. e.g. whether you fly BA, QF, CX, QR or JL LHR-SYD you earn the same status credits regardless of class, the difference is you will earn more Avios with BA than with any of the others.
Similarly, if you rarely do longhaul (esp to Australia or DXB to fly on QF metal), then makes more sense to grab BAEC Silver and maintain that. Keep QF alive by crediting one flight every 18 months to it.