Which is worse in terms of pain, a crown, root canal procedure, or extraction?

Extraction: Crowns and root canal therapy can usually be done without any pain during the procedure and often none (or little) after as well. Extractions always have some degree of discomfort afterwards although the actual extraction should be painless. Always some exceptions.

Still can vary...: Although any of these can vary, most likely, the extraction would be worst. However, with that said, even that pain could be mild and perhaps last only for a few days. There are many variables, many other details that may make the answer differ. When managed properly any of these can be very tolerable if one is open to cooperating with the circumstances and is willing to work with it.....

None of the above: To clarify my answer i must explain that there are three "zones" of pain you are confronted with. There is the pain before, during and after treatment. The preoperative pain is treated by the procedure, the procedure pain is treated with anesthetics and the postoperative pain by analgesics. In all three cases your pain should be well controlled and minimal in experience. Good luck.