Honestly depends on your needs.
Mate 10 is geared toward photography while Note8 is geared toward those who require the S Pen. So if you prioritise entertainment and photog then Mate 10 is for you. Otherwise if you favour productivity, go for the Note8.
This short explanation ignores the differences in price of the two phones. Note that Note8 carries more front facing features than the Mate 10. But on the back it's mostly the same if you ignore megapixel count and functions of the dual cameras between the two devices.
I shan't sway you or anything, you make the call yourself. Personally I'm a die hard Samsung fan so I'll still stick with Samsung no matter what.