Upon casual listening, there is definitely some similarities. The tempi are close, but that can’t be copyrighted. The chord progressions are similar, but you can’t copyright that either. 

But what if we take a closer, more musicological view?

Fig.1 is a transcription of the Satriani piece during the “Chorus.”

Listen for yourself. The melody, played on guitar, should be your focus at 00:49.

Fig. 2 is the “Verse” of Coldplay’s Viva La Vida. While Coldplay perform their song in the key of F minor, this excerpt has been transposed to the key of B minor so that comparisons can more easily be made.

Here is the Coldplay tune. Check out the vocal melody at 00:14.

The chord progressions are nearly identical: Satriani uses Emin9 as his opening chord in his theme. Coldplay utilized GMaj7, the relative major alternative chord. 

The melodies are identical with the exception of the vocal “pick-up notes.” The note choices in the main theme are likely the catalyst for the lawsuit. Though not earth shattering, the note choices on these chords are not “everyday rock radio” choices either: The use of the F# (the 9th of the chord in Satriani’s tune and Major 7th in the Coldplay version) is a chord extension as is the E on the Dadd2 chords. These are choices that would be typical of  a more informed musical ear and somewhat less probable of sheer coincidence.

Personally, I think Joe’s case might just have some traction to it. Then again, in the history of popular music–there are plenty of far more egregious examples: Think of almost any hip-hop tune… no offense–but seriously…

What do you think?