What hurts more a root canal or having a tooth pulled?

Depends. I am guessing that you have pain of dental root origin and your dentist suggests a root canal versus removal of the tooth. If the tooth is in bad shape, extraction might be in order. But if the tooth can be saved (unless it is a wisdom tooth), then a root canal which can be done painlessly, will save your tooth which has significant benefits. Discuss with your dentist.
Neither. Both procedures are relatively painless as long as there is complete local anesthesia. Even after the procedures either one can have minimal discomfort.
Both pain free . Both extractions in root canals can be pain free most of the time. Unfortunately, you only hear about the bad cases from friends and relatives. Most of the time, however, very little pain is involved. This, of course, varies from person to person and tooth to tooth.