Shadow & Waluigi's winning animation, from 'Mario & Sonic at the Rio 2016 Olympic Games on the Wii U. Footage by Zephiel810 https://www.youtube.com/watch?v=6Dv37tUPrlU
these two seem to be the main events when it comes to the olympics, but their rivalry is all friendly, don’t worry
(click/tap for better quality, more rambling below)
Both Mario and Sonic mainly focus on athletic events, specifically the 100m, 4x100m relay, hurdles and the triple jump. Mario, however, is much more skilled in this last one than Sonic.
During the events, they put up the front of being friendly rivals and show off to eachother (Sonic more than Mario), but outside of these, they seem to be the best of friends. They always support/cheer for the other when they aren’t in the same events, and Mario seems to have accidentally adopted this younger hedgehog on the way (Sonic refuses to admit he sees a father figure in Mario).
Aside from the athletic events previously mentioned:
Sonic enjoys skateboarding
Mario enjoys the swimming events, badminton, and boxing