I've used Trinity Guildhall and I have seen Rock School but never used them.
The TG are the drumming equivalent of what you'd play if you were learning the piano. It's a graded syllabus and the way they're generally used here is that you would perform 3 pieces, plus theory, rudiments and sight-reading in an exam. You'd become a very proficient music-reader and competent technician, and you'd encounter a range of genres, but they aren't very closely related to real actual drumming that you would be required to do in a band, and especially after Grade 6 they seem to become difficult simply for the sake of being difficult - but that's what stretches your musicianship, because if you can make them sound like music it's one hell of an achievement.
From what I know of Rock School, these books are intended to bridge the gap between informal drumming and being a trained drummer. I don't know if they cover any styles other than rock, but like the TG, they come with CDs of the pieces both with and without drums.
The first couple of books of both would definitely be worth a try. If you struggle, play one bar at a time with one limb at a time until you're comfortable and then add in the others, and I'd suggest recording yourself once you start to play along with the tracks. Don't forget that there are apps that can slow them down for you, or loop the difficult parts so you can play them over and over.