I presume these are AA batteries? I can't find anything above 2850mAh from any manufacturer that I recognise. There are some higher capacity claims on ebay and the "ship direct from China" websites, but I don't think I'd trust such claims.
Anyway, usually the trade off is self-discharge time vs capacity. So a 2850mAh battery will go flat, on its own, much more quickly than a 2000mAh battery.
(Edit. I am assuming rechargeables here.)