I don't think that it is as horrifying of a MU after sheik. Near release, for sometime I believed that Yoshi had the +1 advantage over ness, but now I suspect that it is about even for both sides (as discussed on the
Ness boards too). Below I linked a close Bo5 set I had with a friend that mains ness, its from a few months ago, but I think showcases each character's strengths and weaknesses.
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Eggs are killer in this matchup. They cannot be absorbed and help us immensely to approach. A mixture of ETS and SH ET should be able to put enough pressure to keep him in shield and we can then follow up with an egg lay, or if the egg connects we can land with a nair. From an egg lay we could usmash/fsmash, or toss an egg, upon release a smart ness would either dodge/nair to prevent any more damage. If he gets too close to the ledge, you could consider trying to egg lay him off. Also, if you're a sniper, you can try to egg his recovery as it shortens it and he falls to his doom (I've only done this a few times ever).
Nair is an amazing tool for us because it breaks through ness' jab string (unfortunately not for his fair). We can also juggle using utilt -> uair. A ness does not ever want to be above yoshi so use that to your advantage.
Ness has an amazing fair as well as a decent dash attack against us. We cannot do much to challenge the fair and his dthrow -> fair is usually guaranteed. I would suggest to just DJ asap and reset yourself to a better position. His uair (big head hitbox) and bair are kill moves, so be careful at high percents. The same goes for his Bthrow, avoid it like the plague and try to keep your landings as safe as possible.
PK fire is not as good of an option for ness because of the endlag and the fact that we can reliably just DJ out and away (and maybe punish). Be wary and just avoid getting caught within it. PK thunder is wicked good for him, especially when we're off stage. We can try challenge it with a nair or dodge, but its fast speed means we probably might get hit with it a few times. If you do get hit by it, try to avoid drifting into your opponent as it is a free uair for them.
As for stages, I don't think ness has that many inherently bad stages (might have to consult the ness boards for this). I think platformed stages would help a bit more for yoshi than it would for ness. If he is on the platform we can shark from below with utilt, usmash, uair, etc., while he can't do too much if we're on the platform. I guess a stage like lylat would also be bad because the stage tilting screws up pk fire.