Evidently the song's writer (and Robyn's regular collaborator) Klas Ahlund channeled his inner Benny Anderson, and saw (his wife-at-the-time) Bruna's record as just ver. 1.0 of the song. Robyn's version adds:
- the scatty B-section ('If you do me right, I'll do right by you...there'll be time for that too') of the verses
- the whole chorus/central tension of the song (yes you can HwM/But don't go falling in love with me)
- the little key-changes to bridge out of the chorus
And here's a snippet of it performed on Gossip Girl:
R's HwM is the finished version (ver. 5.2 perhaps) of the underlying song: it's what others will now cover, not the 2003 original. It would, however, be interesting to hear a hipster lo-fi cover of the full/finished song. Does Paola Bruna do one?
Note that the underlying song is further improved from its acoustic version on Body Talk v.1 to the dance-pop version on BT v.2. E.g., the first couplet is ingeniously sharpened from 'Will you tell me once again/How we're gonna be just friends' to 'Pray tell me once again/...' That slight archaism (used idiomatically and non-religiously but nonetheless colored by its religious associations) is not just the perfect short syllable for the song, it also resonates with pop history (like a living on a save a little save a prayer) and with the church-singing that public singing about romantic love grows out of in the West. Further, there's a touch of an aria from a popular Bach cantata in Robyn's n-part harmonies in the dance-pop version's choruses, as if to confirm that the late lyric change is on the right track, but all of that remains to be figured out. For this and other reasons (e.g., it'll be quite an achievement to play a good approximation of dance-pop HwM's arpeggiation manually), I suspect that HwM is going to be huge with geeks at conservatories.
In sum, HwM exhibits always improving/refining song-craft of a very high order. HwM also demonstrates that a non-native English-speaker's command of English can be better than almost all natives' where it counts, while the non-native speaker's distance from the song's language can nonetheless occasionally allow him or her to make interesting, rule-breaking discoveries, e.g., 'headlessly'.
In some respects the big trick here is one that's very familiar, and that many of us associate with Bacharach/David and with Abba and with Quincy Jones (producing for Lesley Gore as well as for MJ): pop music is music for kids - for the kid in all of us - but it's often done best by people quite a bit older who really know what they're doing both musically and lyrically (Ahlund is 39, Robyn is 31, and her band's members aren't spring chickens). Such figures can end up making something slightly paradoxical: stellar music for kids that's exhilirating precisely because it's so pregnant with adult-apprehended meaning and technique.
 The couplet recurs in the pseudo-'middle eight' of the dance-pop version. The acoustic version of HwM in fact never quite solves its own middle eight problem: a kind of jerk/hiccup in the strings and in Robyn's vocal gets us back to the final double chorus. What would Uncles Benny and Bjorn say about that? I therefore conjecture that (i) fitting the song into dance-pop's more metronomic frame created the opportunity and pressure to better solve HwM's middle eight problem, and that (ii) that led the writers to reuse the opening couplet, which in turn recommended the couplet's last lyrical polish. At any rate, the final version of HwM is near-mathematically perfect and beautiful. In my view it's going to reward a lot of subsequent study, much as, say, Promises Promises, Dancing Queen, and Rock with You do.
 It would be interesting to think through witty tracks like Robyn's Fembot from this dual, super-competence+distance perspective.
 Moreover, HwM's natty video successfully testifies that Robyn is one of those rare pop-figures (Elvis, Beatles, Jackson 5, Abba, MJ, Madonna, Gaga) who appeals to children, teens, hipsters, adults, grandparents...