Clicked on links but what are you saying they are telling us about the demographics?
Barnsey one indicated 92% of central Barnsley born in UK but can't see (might be being thick as usual) any similar data in the Rotherham link? AS I understand it the demographic break down of Barnsley and Rotherham is very similar
https://www.citypopulation.de/en/uk/...8__rotherham_/
Interesting to read about how Barnsley have improved their town centre whilst Rotherham seems by consensus (at least on here) to be relatively poorer. I wonder if it is just a more effective council make up is the difference as so much else seems very similar.