I’m not a dentist but I am a high anxiety patient that has been in this situation a few times.
I’ve always been told by dentists that it’s better to save the tooth with a root canal (and I agree as a patient). Root canals can take a while but they’re painless. You shouldn’t feel anything. The ones I’ve had done have taken about an hour to hour and a half. I’ve personally never had pain afterwards either. You will most likely have to get a crown on the tooth though.
I’ve also had a couple tooth extractions. My extractions have been much quicker than my root canals. I recently had one cut for extraction like your dentist explained. You shouldn’t feel any pain, but you might feel pressure and hear some noises as they’re working. Afterwards, you’ll likely be sore and you have to be sure to properly care for the area. The dentist will likely suggest getting an implant so your teeth don’t shift later down the line.
Overall, I personally prefer to do a root canal and save the tooth, but either option is perfectly fine. Both seem scarier than they really are! Whichever option that you choose, try to relax. I find focusing on my breathing during my appointments helps. Both of these procedures are safe and your dentist does them everyday. Although it seems scary to us, there really isn’t anything to be scared of. You will do great!