In "Royals", there is one part that stood out to me the first time I heard it. I immediately recalled the 8th track ("Home") from Dream Theater's "Metropolis Pt.2 - Scenes from a Memory" album. The similar sections are: In "Royals" - the hook after both verses (e.g. "gold teeth, grey goose, trippin' in the bathroom") and in "Home", the 1st verse ("Shine...lake of fire. Lines...take me higher"). Both sections are in D maj and the bpm is about the same. While the melodic line is different, the harmony is the same. There is also an absence of ringing instrumentals in both songs (only a chopping guitar riff in the Dream Theater song) so it feels similar too. [Home (2:38) and Royals (:33) -- ed. furtherlane]
In 1977, the Starland Vocal Band won a Grammy Award for "Best Arrangement for Voices" for its sexually-suggestive number-one single Afternoon Delight (released April 1976). SVB hailed from Washington, D.C. That same year, singer-songwriter Jason Mraz was born in nearby Virginia. Coincidence? The bridge to Mraz's love song I Won't Give Up (released January 3, 2012) features the same chord progression (2-5 or F#min7->Bmaj for IWGU, and Gmin7->Cmaj for AD), vocal melody, and harmony as the pre-chorus to Afternoon Delight. Compare IWGU (around 2:16) starting with the lines "I don't wanna be someone who walks away so easily, I'm here to stay and make the difference I can make", to AD (around :27) with the line "When everything's a little clearer in the light of day." Hard not to picture Ron Burgundy's news team singing it!
London's folk rock band Treetop Flyers derives its name from a U.S. helicopter platoon known for flying low-altitude missions during the Vietnam War (and not from Stephen Stills' track Treetop Flyer). The band's affinity for things old and American also extends to its May 2011 single Things Will Change, which borrows heavily from the U.S. folk rockers America and their 1972 hit Ventura Highway (e.g. G maj7 to D maj7 chord progression, vocal harmonies). Check it out.
For me the similarity is mostly in the vocal lines, where Billy sings "Oh oh oh oh" (around 2:40), and Pink on the choruses sings "Ah ah ah ah, sun is blinding" (around 0:26), as well as the production value (i.e. the heavily reverbed snare), vocal lines doubled an octave apart (a la Righteous Brothers and a million Motown/Philly Soul records).
Need You Now won three Grammy Awards in 2011, including "Song Of The Year," and "Record Of The Year." Eye In The Sky was not even nominated when it was released in 1982. Parsons is best known for his audio engineering/production work on numerous Abbey Road Studios recordings including Pink Floyd's Dark Side of the Moon.
For music theorists:
Part of the similarity, stems from the fact that both songs progress from a major tonic chord to a minor third chord for two bars each in the chorus (in the case of Need You Now, E major to G# minor; in the case of Eye In The Sky, D major to F# minor).
Need You Now (1:07) VS Eye In The Sky (1:28)