Greetings,
Yet, I'd argue that Kings Cross and It Couldn't Happen Here are very different from Birthday Boy. They're in an entirely different league.
The main problem is that Pet Shop Boys never really found a way to consistently integrate synths and guitars in a way that New Order successfully did. I suspect this is because Pet Shop Boys arrangements are more often chord-driven, and that Neil's voice typically serves as the lead instrument in its own right, rising above the backing. On Birthday Boy, we encounter a mix of guitar arpeggios and synth pads... and to my ear, it's a little bit muddy. Compare this with the majestic, wind-swept spaciousness of Kings Cross and the lush orchestral score of It Couldn't Happen Here.
New Order's arrangements are usually different in that they tend to involve an alternating sequence of lead hooks (no pun intended) by different instruments. Synth chords don't seem so prominent in the mix, and there's less layering. The exception to this rule is Regret, which showed that synth chords and guitars can be integrated well. I guess achieving this integration is easier in practice, when you have actual guitarists in your band who contribute to the writing of the songs, rather than just ring-ins.
Retro.

"Politics are too emotional now. Contemporary culture generally is too emotional, really... I'd rather people looked to the truth." (Neil Tennant)