Neither of these options is better than the other; it’s a decision that can only be made on an individual, case-by-case basis. What is important is that you have a healthy tooth. If extraction is the choice, then the tooth should be replaced with a false tooth, bridge or implant.
If you allow a dying tooth to fall out on its own, it might take a lot longer than you think. And during that time, the decay from that tooth can spread to other teeth. The injection for anesthesia before a tooth extraction might not be pleasant, but the toothache pain you experience from your dying tooth is likely to be far worse, and continue for days or weeks. Sedation dentistry can also help you relax and make the extraction appointment comfortable.
If you’re one of the lucky ones whose wisdom teeth come in correctly, there is a good chance you can keep them, along with the rest of your teeth, for your whole life. However, proper oral hygiene and regular checkups are essential to maintaining the health of all your teeth.