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The smaller capacity one can do Qualcomm Quick-Charge.
Edit: @hippy spotted it. The Qualcomm version is only for certain devices, but does work well. Both batteries can be charged themselves with the Qualcomm Quick-Charge though. Otherwise it's down to the devices to negotiate the charging current. Same way that some wall chargers can dole out ~2A (for tablets) but an old phone won't accept that much.
Why is the 10000mah almost the same price as the 13000mah battery?
https://www.amazon.co.uk/Anker-PowerCore-Recharges-Portable-Chargers-Black/dp/B012SRLKZ6/ref=pd_sim_107_3?ie=UTF8&dpID=311cCeTs9eL&dpSrc=sims&preST=_AC_UL160_SR160%2C160_&psc=1&refRID=AKG93ZZMDHWA4TD9JBR8
https://www.amazon.co.uk/Powerful-10000mAh-Anker-PowerCore-Technology-Black/dp/B012SNMWCK/ref=pd_sim_107_4?ie=UTF8&dpID=318xDxnwgdL&dpSrc=sims&preST=_AC_UL160_SR160%2C160_&psc=1&refRID=FV94PQZN1G5MJN1XMZCB
Does the 10,000 have some feature that makes it better? They both appear to be the same model just varying capacity.