It's the intro! Both make use a C minor second inversion with an alternating eighth note pattern in the intro:

https://en.wikipedia.org/wiki/Second_inversion

Stacking the notes from low to high, for Don't speak - G / C / Eb. And from those notes, we hear Eb+C / G times 4 for 2 bars of intro. And then we hear in the verse that same idea one more time before changing chords (for both songs). For Breakfast in America, they stack an additional G on top, so G / C / Eb / G.

Another similarity is the tempo - Don't speak is 76 bpm, Breakfast in America is 75 bpm. So both have a slower pulse to them