I agree that other than concentration, and possible other additives, chlorine bleach is all pretty much the same. I would not purchase liquid chlorine bleach that doesn't list the concentration. And if one gets a generic version with lower concentration, why not just use more of it? Not hard to figure out how much more might be needed, presumably.
Myself, I rarely if ever use chlorine bleach in laundry. I do have some in supply but for other tasks, such as disinfecting something really nasty. Or getting out stains on non-fabric objects, like concrete or plastic. I cannot remember the last time I needed to do, that, anyway.
I find STPP and hot water does the job w/o the need for any bleach.