Umm, depends what you use your tablet for.
General use like browsing, video, reading, viewing images, facebook, netflix, youtube and some minor gaming than a Galaxy Tab S would work well for you.
If however you play a lot of 3d games and enjoy smooth framerates you should definitely go for the nvidia Shield tablet as it's around 2-3 times faster, for general use it's very good also but lower resolution than the Tab S display.
Nexus 9 uses a slightly faster version of Tegra K1 but does have a higher resolution to work with so it might end up a little slower than the shield when you take display resolution into account for gaming but otherwise should be very fast. Also the display uses a 4:3 ratio so it's not going to work well with your widescreen content.
Unsure how Android apps and games deal with devices using the 4:3 display ratio, might be a bit messy until they update.