Main differences from what I can tell:
-Faster loading times
-Better resolution (Wii U had 720p while Switch has 1080p) (Switch will revert to 720p when in handheld form)
-Framerate increased from the really weird 59fps to nice, smooth 60fps-
-DLC included
-Everything unlocked from the beginning (except car part and a character)
-You can now switch cars when in online lobby's (in all previous online mario karts, you had to disconnect in order to change your kart)
-Fire hopping removed (a technique used in the Wii U version to increase boost times by exploiting mechanics)
-Third tier of boost added (blue, orange, purple)
-Can now use double items and hold two items at once
-Dry Bones, King Boo and Bowser Jr added
-Inklings added
-Battle tracks removed
-Battle courses added
-four battle modes added
-Boo item added
-feather item added but battle mode exclusive
-Tutorial section which explains a lot of things
-New alternate title screens after starring everything
-200cc time trials added