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yes, the chinese cheapies do often overrate the mAh rating.
No, they don't always.
Yes they are often as good or better. If anyhting my experience has been that the ones with a higher Ah rating tend to havbe a higher failure rate and loss of ability to retain a charge after a year or two. But in the short term they are just as good.
Some of the chinese cheapies specify that they use a particular high quality japanese cell in their china assembled batteries. Those are probably the ideal ones to get.
I found recently in Australia that betterbatt imports a specific type of chinese batteries becasue they are up to local quality standards. They are the same ones I got from china a few years back. I'm ok with buying them locally now becasue they arrive quicker and it's much easier to get any warranty replacements. Incidentally: they are labeleld with a more 'true' mAh rating (more pessimistic). Which is still higher than the official name brand ones. Though in reality they are probably almost identical in terms of output and lifespan. Just much cheaper. Yet somewhat more expensive that the identical chinese ebay ones that may be really old.