Mike: As Chuck said, wiring in series is better than wiring in parallel. When you split the circuit path between the 2 LEDs, you end up dealing with 2 independent calculations for voltage and current. So if the forward voltage of the LEDs do not match, you'll end up with different current as well and that could cause the LEDs to shine with different intensity.
Series wiring is the recommended method. That way the current moving through the 2 LEDs will be equivalent and the forward voltage (which may vary due to manufacturing technique) don't have to match exactly.
Yes. Your previous diagram showed the LEDs wired in parallel; each LED having a positive and negative to the supply voltage. Your last diagram shows the LEDs in series. That's the way to do it. That's the recommended configuration.
