Definitely a great drummer, but the first music piece I will always associate Neil's drumming work is not with Rush, but actually with one of the pieces on Jeff Berlin's album. The song fits Neil's playing style and I can see why Neil was hired for that one piece even though Steve Smith (Journey and other groups) could have played it just as well.
Jeff Berlin Champion (Of the World) Neil Peart Scott Henderson
Jeff Berlin Bass Scott Henderson electric guitar Neil Peart Drums
Neil Peart's drumming was good, but the drummer that went way too early imo (1993) was Jeff Porcaro. Jeff did truckloads of recording sessions with a wide variety of musical artists besides Toto. Jeff was the "drummer's" drummer. iirc one of the guitarists tribute to Jeff was quoted: Jeff would come in. He would listen to one of my songs before doing the drum track recording and would play it perfectly the first time he heard the song and his drumming style would fit my song recording exactly the way I wanted the drumming to be played.
That testament alone is why Jeff was hired by lots of artists.
I don't recall if Steve Smith or maybe it was Jeff Porcaro that did the drum work for 20000 prayers.
While in high school during early 1980s years and some classmates were Rush fans, I and a few of the other high school marching band snare drum line members would head up to LA area to North Hollywood, CA Bake Potato joint. And watch the musicians that made up the group Dog Cheese perform at Baked Potato when they were not on tour with Joni Mitchell back in early to mid 1980s.
As for guitarists, I liked Allan Holdsworth, Scott Henderson, Pat Metheny, but Michael Landau is tops imo. One of the reasons I liked Dog Cheese besides Vinnie Colaiuta's drumming.
Dog Cheese (Michael Landau, Vinnie Colaiuta, Steve Tavaglione, and Larry Klein)