Who gains more the benefit(s)? The composer or the one who performs the composition?

Depends on how you define "benefits." The composer is paid a fee every time her song is performed. True, it's a pittance when compared to how much the performer may earn in the course of the performance. But the composer's product, if you will, is like an excellent investment. It just keeps paying dividends.

If you define "benefits" as artistic development and growth, then the performer more than likely derives more, because he is probably expanding on the original concept in the way the song is arranged and delivered. In fact, the composer may actually lose, if a song is interpreted by a performer in a way that's dramatically different from what the composer intended.

If you define "benefits" as fame, then initially, at least in my opinion, the performer wins. It's only after a particular composer pens many hits (or well-received compositions) that she is recognized, typically. In ancient pop history, Neil Sedaka or Carole King come to mind. Both were successful composers who didn't "arrive" as performers until other people had performed many of their compositions.

The performer does. No one cares about the composer.