If you are ok with spending a few more dollars, I would definitely go with the Note 8. As someone showed earlier with the specs, the Note 8 has more RAM, which is a huge deal when talking about how much we use our phones these days. The more RAM, the more you apps can be used and the longer you can use all those apps, without the phone getting bogged down, and slowing to the point of needing restarted.
A couple other differences between the Note 8 and the S8 are the Note 8 comes with the S-Pen and has a dual 12MP camera. The S8 does not have either of those additions.
Here's a pretty good video that compares the 2 phones, I'd definitely check it out. I think it will help you make the best decision for you: