Please convince me Master Yi is better than Udyr

I'm pretty good with Udyr so far. I like split pushers who can control the game and put the team into a position of victory even if they fed horrendously and can't seem to coordinate. I actually enjoyed Jayce in this role too, but find him to be much more difficult to pull off compared with Udyr.

Unfortunately for Udyr, Master Yi has the best skin the game now with Project Yi.

I find Yi a competent split pusher. Although I haven't had as much success as with Udyr. It seems the main reason Udyr works better is because I have a basic ability movespeed buff to keep me going rather than having to rely on an ultimate. I also have a stun that can secure me kills without having to use an ultimate. It also seems to me like udyr becomes dangerous much sooner in the match.

Yet, I know Yi is good. So I come here seeking reasons why I am wrong, and despite Udyr's insane winrate, that actually mastery Yi is the superior champion and he is the one worth investing my time in so I have an excuse to use the Project Yi skin....