I probably have THE most Fox/Yoshi experience of any Yoshi here. My best friend is a Fox main and has been since the day the game came out and we've been studying and playing the match-up for well over a year. I stand by my experience and say the match-up is 55:45 Fox. The main reason/s I don't say the match-up is 50:50 is because the reflector can break up Yoshi's combos and Fox is so much faster that unless you predict most of what he does, Yoshi gets punished easily.
Fox's up-tilt only hits twice before you can get out of it. The Yoshi just has to jump and about 25% of the time, Yoshi can get a neutral aerial off in the middle of the hit-stun. What I usually do is try a neutral aerial after the first up-tilt and if it doesn't work, then I jump out of it while absorbing the 2nd hit.
Fox only has 3 reliable kill moves against Yoshi: back aerial, down smash, and up smash (of course). The down smash is usually done after a down-aerial connects and Yoshi is near the edge. The up-smash is used as dash, follow-up to the down aerial, and jab-cancel. Proper DI and Yoshi can live a fresh up smash at 115% Any higher and you have to hope the move is decayed slightly or you'll die. The back aerial is insanely quick and you just have to predict it to avoid it. Proper DI can have you living at about 120%
Keeping pressure on Fox will keep the laser camping down to a minimum. Yoshi cannot outcamp Fox period so don't even try. Ledge camping on the other hand is beautiful. Especially if you vary the lob of the egg throws so that they hit at different times. The reflector makes Fox have a little bit of lag afterwards if he reflects something. So a viable strategy that I've used MANY times is to throw an egg to bait the reflector. If he reflects it, you can counterattack before he can recover from the stun.
If a Yoshi can grab a Fox out of his 2nd jump over the edge, it's a guaranteed KO. Once the Fox breaks out, you can jump off stage and do a down aerial which will push him low enough to where even if he uses the up-B again, he won't make it back to the edge. This is easier said than done though, because most Fox players will combine the 2nd jump with the forward aerial to get the added height and protection. The priority on this move (compared to Yoshi) is pretty good and is hard to stop, but you can time a grab/forward aerial to hit him out of it.
Mainly, a Yoshi just has to stay close to keep pressure and to avoid the damage from short hop double laser camping. The hard thing is knowing what to do against each attack in close range.
The down aerial should be shielded and depending on what the Fox does, should be followed with a grab, side dodge, or roll. If the Fox short-hops again, then another down aerial is coming and you should roll out of the way or you'll risk getting caught in a loop that'll severely weaken your shield and cause you to do something you normally shouldn't. If the fox lands next to you, a side-dodge is probably the best bet because he'll most likely follow it with a grab, up-tilt, or up-smash and all 3 give you the opportunity to counterattack before he recovers. A shield grab can be done but only if you buffer it and absorb the final hit from the down aerial. Since Yoshi doesn't have a chaingrab against Fox and his throws don't do that much damage, I'd avoid this unless you're near the edge and want to put the Fox in a bad position off the stage.
Whenever Yoshi egg-lays Fox, the Yoshi should sprint the opposite way and do a sliding up-smash to hit the egg. No matter how fast the Fox breaks out of the egg, this is guaranteed, and with proper spacing, you'll be just out of range of his attacks when he breaks out, so you'll be safe.
I think that's all I can think of at the moment.
I still stand by my experience and say it's 55:45 Fox
Down air to smashes only works at certain percent thresholds, certain cancel windows, and from trips.
and I'm a Fox player... Up-smash is an amazingly good finisher, but the other ones mentioned above are great.
