Both sevoflurane and isoflurane are used on humans. Sevo is the newer of the two and I believe is more widely used now....
Sevo causes less irritation to the airway and gives a faster rate of induction and recovery, but less iso is metabolized by the liver and kidneys.
Here is an edited version of a study done by Oklahoma State University on inhaled anesthetics.
They're BOTH safe for your dog... I'd choose the vet you you trust and are more confortable with.