Fox and Sonic's neutrals aren't that amazing compared to the tip top ones.
For best neutrals off memory I'd say it's something like this, in no order:
Mewtwo has an amazing reward off touching you with any of his neutral tools that are relatively safe
chargeable projectile that can be canceled rockets you up there, and the fact that it increases mobility while doing absurd damage(what is it, 26%?)
Good mobility
can kill you or do +20-30% for touching his shield
good jumpsquat
Very big hitboxes with good damage
Decent/good options out of run
Short hop airdodge is ridiculous
His approach options aren't amazing, but like Sheik he almost never has to approach so that doesn't matter
good at converting to death situations once he wins neutral
says "nah" to most attempts at shielding
It's like a Bayo thing where his neutral may look weaker than the others in the top 5 neutrals on paper, but the risk reward is so heavily skewed in his favour that it pushes him up there with the best.
There's quite a bit of incorrect or misleading stuff here.
Shadow ball is not limit. It doesn't affect his mobility.
Besides a 13% throw, kill throws, and up smash, Mewtwo's fastest out of shield options are a total of 11 frames for forward air and 12 for neutral air. Forward air and neutral air are the only ones with any chance of doing 20-30%, but why would you get on the character for the enemy misspacing an attack that badly? Mewtwo has bottom-tier traction. Hitting his shield safely isn't that hard. Also, frame 11 for an out of shield option is pretty mediocre. Down tilt isn't an out of shield option, though it would only be 1 frame behind neutral air. However, you won't get 20-30% off of it if you don't hit the base of his tail. Consider that with his bad traction.
What hitboxes are that large? Down tilt? I guess it's pretty big, but only the base combos beyond a simple forward air, so it's not that big of a deal. Up tilt is pretty big, I suppose. It's totes unsafe, though. It can at least combo into an aerial if you get the right hitbox. I guess it's a decent anti-air. Back air is his biggest aerial, but it's frame 13 and extends his hurtbox before it even comes out. It also has the inverse tipper while being unsafe on shield up close. You could autocancel it to make a retreating base hit back air safe, but, like.....why? Up air reaches about as high as Captain Dashgrab's, so if you consider that very big, no comment. The hitboxes don't even exactly match the animation, though that isn't a big deal. Forward air is not a big hitbox. Neutral air loses every trade, so who cares?
Confusion is his biggest disjoint in the front. It does 9% and leads to nothing.
Mewtwo has 3 options out of a run that are any different from the rest of the cast: confusion, shadow ball, and jump-canceled up smash. I mention up smash because he slides far. It's in no way safe. Confusion is worthwhile only for retreating, and it's just 9%. Shadow ball is good. Wavebounce/b-reverse it, and you have a totes safe on shield 25% killing hitbox-beating shield-slamming projectile that moves you forward or backwards.
Mewtwo has only 3 combos of which I know that actually convert to death, two of which require the inconsistencies of neutral air: down tilt-neutral air-up air-forward air at the ledge (works at like 30% on Shiek), down tilt-forward air-up air-forward air also at the ledge (also at like 30% on Shiek), and landing neutral air to up smash/ up throw (at, well, kill percents).
I suppose one could use the last hit of neutral air to lead to a kill move by autocanceling it, but that's so easy to see coming and just shield that I don't think it should count.
Mewtwo really only solidly beats shield at kill percents, when up and back throw are relevant. Blocking a fully charged shadow ball won't break your shield. However, it comes out on frame 23, so it's not TOO hard to dodge. It's frame 6 from the charging animation, but that leaves Mewtwo immobile. I wouldn't call taking like 15% from a pummel and a throw saying "nah" to shield. It's decent damage.