Current will flow between the batteries based on the difference in terminal voltages, not based on the difference in State Of Charge (SOC), and certainly not based on absolute capacity (equal mAh remaining). The terminal voltage vs. SOC curve is highly dependent on the chemistry and manufacturer of the cell, so don't assume that two cells will behave the same even if they have the same nominal voltage. A typical voltage vs. SOC curve for a Lithium ion Polymer cell looks like this:
In short, while you might succeed in moving a little charge from a full cell to an empty cell, current will most likely stop flowing between the cells well before they have equalized SOC, and they'll never end up a the same amount of stored energy remaining given that they're different sizes.
If you want to use one battery to charge another battery, consider a boost regulator in conjunction with a charge management IC. In your application, you would use a boost regulator to get to 5V from your external battery, then use your normal USB charger to leverage the existing charge control circuitry for you phone. You won't even void your warranty!