I would say do the root canal.
Dentists are all about saving the tooth, but doing the least invasive thing, first. So a root canal would leave the original tooth, but remove the roots.
An extraction is more of a not-good thing for your mouth, because then it leaves a space, and your matching tooth (if the pained one is on bottom, then I mean the top one above it) won't have anything to "bite down on" when you close your mouth, and... I am not explaining this very well.
But it upsets the way your mouth is structured, and contributes to bone loss, unless you have an implant done, which is WAY more expensive than a root canal. I have a couple of those, too.
I have had several root canals, and they are nowhere NEAR the pain and trauma, IME, that they're hyped up to be.
My first one, I was in and out in 45 minutes, feeling no different when I left than when I went in. It was a front tooth.
My other was a side rear one, and it was a little more difficult, but still no big deal.
What I do is this: I have them rub the numbing cream on my gum. Then when THAT takes hold, they can do the novocaine shots. I get lots. I never ever look at them or the equipment while they work. I close my eyes and go to my happy place, or look away. The novocaine needle is intimidating as all hell. Don't look.
Then when I'm all numbed up, they do their thing.
If they say I can, I take ibuprofen ahead of the game, so I don't have super-pain when the novocaine wears off.
Hope that helps