This all depends on portability. Do you carry your tablet everywhere you go? I personally don't and therefore find the Note 8 to be more convenient. Note 8 also has a better display than the Tab S3, along with better camera (obviously), and more RAM. Great for multitasking.

Another thing is that you can use the Tab S3 S-Pen on the Note 8. You can buy 'standard' size S-pens from Samsung or even Staedtler. All you have to do is disable the S-pen power saving feature and you can use any S-pen device on the Note 8 even if the actual S-pen is inside the device. You'll have to carry that 'standard' size S-pen separately though.

Anyway, it all comes down to your preference. Some might find the Note to be a bit small for full-fledged note taking. For that purpose only, I think the Tab S3 (or even something like the iPad Pro with Apple Pencil) is better simply due to their size.