You have two identical cars, both with a full tank of gas. You drive them on the freeway side-by-side at identical speeds. No matter how closely the experiment is controlled, one car will run out of gas first. The other car may run out of gas soon after, or it may go for many miles before stopping.
There are many variables in battery manufacturing; no two batteries have exactly identical capacity. Like the cars, one will run out first even if they are discharged identically. If you are using cells from a reputable manufacturer, it is reasonable to expect that their capacities will be reasonably well matched. In this case, the remaining capacity in the cell that is not depleted should be small.
There are also variables associated with battery discharge that may exacerbate the issue, though these may not apply to your situation.
For example, some battery powered devices require different supply voltages internally. A cost-effective way to do this is to 'tap' the battery pack - Two series AA cells can supply both 3V and 1.5V, but in this configuration, one cell will supply the load current for both supplies, while the other cell will only supply the 3V current. In this case, the cell providing both supplies will always be depleted first.
In some devices, the physical location of the cells may cause one cell to be externally heated more than another (imagine one happens to be right under a heat-generating IC, while the other is near a keyboard). Two identical cells under the same discharge current but at different temperatures will have different discharge characteristics.