couple weeks. Symptoms will be headaches, body aches, cough, sore throat, maybe a mild fever, maybe loss of smell/taste. But on average, not worse than a cold. However, if you get sick you'll be contagious and can spread it to other people. So that means you'll need to quarantine for at least those 10-14 days that you're feeling sick. You'll have to miss work, school, etc. And your family will probably also need to quarantine to some degree as well.
If your symptoms are worse, you might get very fatigued, have terrible aches and pains, difficulty breathing, high fever, and other symptoms that may persist even after you're no longer contagious. You may have to be admitted to the hospital. And you'll still have to quarantine.
If you get the vaccine, best case scenario is you'll have no or mild symptoms for a day or two at most. This will involve aches and chills, maybe a light fever, headache. After that, you'll feel better and symptoms will go away. This seems to be the most common response to the vaccine.
Worst case scenario for the vaccine is heavy fatigue, really bad headache, super achy, high fever. But still, this will probably only last a day or two after which you'll feel better. And this response seems to be uncommon.
So not only will your negative symptoms probably be more mild and last a much shorter amount of time, more importantly you won't have to quarantine for 10-14 days if you feel crummy from the vaccine for a day or two. To me, I'd much rather risk feeling crummy for a day or two vs. feeling bad for a couple weeks and being contagious with a disease that has the potential to make others really sick.