I don't know if poodles are sensitive to anesthesia any more than other breeds, but I do know that the first time a dog goes under is the riskiest time because you don't know if that particular dog has a sensitivity to the anesthesia.
That said, done correctly, anesthetic procedures are quite safe for the most part. Reactions are not typical.
Before Jager is neutered (many months from now) I plan on having bloodwork done so the vet can see if he has any liver or kidney problems. In fact, I am a big believer in bloodwork before any anesthetic procedure, regardless of how many times the dog has gone under. Many vets require bloodwork, and I think it's for a very good reason.