Since discussion has started again, I would like to post what I think are the most relevant. My tier list is as follows:
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Fox--Fox should win vs the characters not named Falco and Marth. However, I think Falco and Marth are both close to even (they can very easily be overwhelmed on small stages, but the larger, flatter stages limit Fox's pressure and allow him to be walled easier.
Falco--should have a better matchup spread than Marth and can more effectively apply pressure with lasers and high priority hitboxes. In my opinion, Falco is better than Marth because he can limit options better than Marth on the ground, but doesn't have a better ground game than Marth.
Marth--Suffers from lack of kill options at high percents like Falco but is forced to engage his opponent because of lack of projectile. Down-tilt while amazing, can be jumped over and punished. This wouldn't be that significant if Marth had a lingering hitbox, but unfortunately, Marth really only has N-air. Marth is also very fragile, and has to be very aware of his spacing, inherently hurting Marth's consistency.
One thing that I've never really understood is his supposedly bad matchups (Shiek, Falcon, and Pikachu). In my opinion, these matchup struggles boil down to lack of consistency (especially in the punish and edgeguarding game), limited use of CC, and improper threat identification. I don't know about Yoshi, though. However, maybe if you just play like a lame jerk enough, you can squirm out a win in the matchup, especially on Yoshi's, FoD, and FD.
Thoughts and opinions, everyone!