The critical parameter to batteries, capacitors, and any power source is the (effective) Series Resistance, Rs or ESR. Generally the bigger the capacity [Ahr] rating, the lower the ESR [Ω].

Here the batteries are graded by ESR.
![enter image description here][1]


  [1]: https://i.sstatic.net/g171d.jpg

In your case, if you are using the same grade and size of battery the differnce will lie in the aging factor and remaining charge capacity which both affect ESR. So you can estimate each batteries current load capacity based on the ESR which must be tested somehow.