Are there any real reasons not to fly AA over BA or to book through AA.com or BA.com?

As I said, I'm just looking for a cheap economy flight ideally earning Avios. TP are unimportant as they're not going to make any difference this year so PE/WT+ or above is immaterial and I'll survive.
Still not sure if booking an AA basic fare through BA.com would earn anything regardless of what it says, but then again, I've the 24hr cancellation window should AA not let me select seats thus indicating I'm getting nothing.

I would like to use the T3 lounges rather than the T5 ones as I've done them to death, haven't used the QF lounge yet and some noodles from CX F would hit the spot.

AA gives me the option of the 787 to ORD (which ticks off another cabin on this aircraft after already flying F and J, just leaving PE) although flying straight to LAX and connecting to SFO lets me use the QF F lounge for a shower and my favourite salt & pepper squid.

The AA website seems to be around £25+ cheaper than if I book through BA.com and can be on the same planes (£375 if I fly the A380 and book through AA; £404 if I book through BA)