Besides the piano vs guitar issue, I believe that Bono's melody is carefully delivered in the studio version... every note, every silence, the cadence... every single thing looks carefully crafted.
That makes the first half of the song very interesting to listen to, very enjoyable.
The live or jamming version, invariably will lose that part, but it'll gain in emotion.
That's my theory on why the first half of the track sounds more interesting in studio at least to me.
Anyway, the song is the song, and that's a combination of both studio and live versions. Even if I like Bad Live a lot more, in my mind is the same thing...