I agree that the resistance of the wire is extremely small and insignificant. But the left battery in the top image has an extra wire between its + post and the + source. And an extra wire between its - post and the - source. Meaning two extra connection points on the positive side and two more on the negative side that the right battery does not have. And those four connection points would have more resistance than the wire. Especially so as they age. Being that any pressure connection is going to have some resistance, the left battery is always going to have slightly more line resistance than the right battery.
On the lower image both batteries have the same number of wire connection points between the + and - sources. One poor connection could still cause some increase in resistance to one battery. But if all connections were good, the resistance to each would be the same. Not so for the top image.
