I use Bison chucks most often. They are accurate,and not as expensive as some are(though lately they have gotten MUCH more expensive). I cannot evaluate all inexpensive Chinese chucks,but I can offer possible flaws in cheap 4 jaw independent chucks: It is possible that their jaws' slots might not be perfectly parallel,so the jaws could be at an angle to the centerline of the turning. Faces might not be square to the centerline(CL). It is possible the bodies may be made of crappy grades of cast iron,too soft to resist the jaws from pressing into the iron with repeated use. I did have a cheap 4 jaw that came with a Romanian lathe,whose jaw screws actually would FALL OUT when I took the jaws loose to rotate then,and that chuck wasn't even Asian!!
It's possible that the threads on the back won't be square to the body,and the chuck could wobble some thousandths so you could never make accurate work with the chuck.
I could go on,but you get the idea. I'd try to buy a 6" Bison if you can. At least test the runout of the face,and parallelism of bars clamped in the jaws. Look VERY carefully where the jaws meet the metal clamped in them to see if you can see ANY light under either end of the jaws. Cheap metallurgy,you can't really see or do much about.