It might be helpful if you share which tooth it is in question.
There are a few implications for the different choices, the greatest factor probably being cost.
With a root canal you are looking at a lengthy process and several visits. Depending on the condition of the tooth and how much damage was done you may need a crown after your root canal.
If your tooth structure is badly weakened you may even need to have a post and then crown. Other surgeries that you may need to go through for crowning might include addition work on the neighbouring teeth, or crown lengthening (cutting away of your gums) to get the crown to fit. All these would not just be a long painful process but also cost quite a bit.
There is no guarantee though of saving the tooth - At the end of the day you might still face extraction. Only your dentist can best advise you.
If you opt for extraction you might want to consider getting a post fitted in to prevent bone loss. This is crucial especially if you are young. If you leave a gap, your neighbouring teeth will drift over time and your teeth will go out of alignment. Your other cosmetics solution might also include getting a bridge done but that would mean work on your neighbouring teeth.
Either way you are looking at quite a bit of money with extraction being the cheaper option. But like some of the other members have said money you can earn back...bone loss and tooth you cannot.
Don't worry too much about severe nerve damage... it's not everyday you end up with that and if your dentist is careful you'll be fine.
Root canal or extraction? This is a personal choice you need to consider and talk through with your dentist. We all have different circumstances and this is a photography forum not a medical one so I'd take all comments with a heavy pinch of salt. Do your own research and come to your own conclusion.
You might do good to google root canal and tooth extraction pros and cons.