Do dogs or cats cause more allergies? We want a pet.

They can. Dog and cats can definitely cause allergies. They may cause asthma too. If u r prone to develop allergies, even if u have no allergy to dogs and cats now, u can develop allergy to them in the future.
Tough answer. Both dogs and cats can cause allergy problems. If one does not have problems around dogs and cats now then it probably ok to get a dog or cat. If dogs or cats cause problems now then it would be prudent not to get a per.