The first wiring method is called "bipolar parallel".
The second wiring method is called "bipolar serial".
The bipolar parallel hookup requires more current but a lower voltage.
The bipolar serial hookup requires less current but a higher voltage.
Or, another way to look at it is that when using the same voltage, bipolar parallel should permit you to get higher speed from the motor (or better torque at a given speed as you increase speed).
One link that discusses this is: UniPolar vs BiPolar wiring schemes for 2-phase Stepper Motors