Most of the time it doesn't change their personality too much, except for the better. However, there are a few instances of a rabbits personality changing for the worse. Whether that is due to the neuter/spay or just due to the stress of the being in the vet office, it's hard to know. I have neutered bucks that pretty much have the same personality as before, minus the hormonal behavior.
I have a few recommendations. Some vets want the rabbit left over night. I would recommend not doing this as it can be very stressful on a rabbit(especially if there are cats and dogs there too) and can be very frightening for them, and can cause problems for their recovery due to the stress. And I would try and drop them off at the latest possible time to limit the stress they are exposed to. I would also find out and try and ensure that they are not kept in the same room with dogs, as this can cause undue stress. Even though males don't usually need pain meds past the first day, I feel it is still a good idea to get enough for a few days, just in case you feel you need them. It's also good to have syringe feeding mix on hand just in case. Then when you have him home, keep him warm and keep encouraging him to eat. I've had the most success with leafy greens, but only if your bun is used to them. Also spend time with him, comforting him and petting him if he'll let you. It's what bonded rabbits will do when one is feeling unwell, and I think it will help aid in the recovery and help relieve any stress from the whole experience. And be prepared to spend 24-48 hours helping him recover.