Shivpuri is the stretch that made Rishikesh famous: 16 km, two and a half hours on the water, and the rapids everyone has seen on video — Roller Coaster, Golf Course, Return to Sender. It is friendly, it is efficient, and it is the right first trip for almost everyone.
Kaudiyala is a different animal. Thirty-six kilometres, four to five hours of paddling, a put-in an hour and a quarter upstream, and Grade IV water in the upper gorge. You are in a canyon with no road noise, and the day asks something of you.
Choose Shivpuri if it is your first raft, if you have half a day, or if your group's fitness is mixed. Choose Kaudiyala if you have rafted before, you are fit, and you want the river rather than a sample of it.
Whichever you pick, the safety standard, the gear and the briefing are identical. The difference is only how much river you get.