Fair enough.
In Earthbound, Ness grows and develops a myriad of psychic powers relating to Photokinesis, Paralysis, Hypnosis, extremely powerful healing capabilities and the ability to summon very sturdy PSI shields which protect against all forms of physical attacks. In the later stages of the game, these techniques become powerful enough to paralyze and/or put all targets to sleep, create flashes of sacred light which obliterate enemies out of sheer power (the move doesn't even deal damage, it just eradicates all targets), and heal all his surrounding allies for such an incredible amount it can bring your whole party from death to almost full health. In addition to this, Ness can resurrect target allies, a skill which is far and above most characters skills in smash bros. In smash bros, Ness demonstrates Pyrokinesis and the ability to manipulate electricity, combined with the ability to use the spell PK Starstorm.
But I don't believe that Ness' psychic powers are more powerful than Mewtwo's when it comes to destruction, but Ness demonstrates that he has healing prowess beyond what he can do for himself (Mewtwo's Recover, he does not learn Wish, Heal Bell or Healing Wish). Ness also possesses the ability to incapacitate multiple opponents unlike Mewtwo (Thunder Wave, Disable etc.) and create barriers that reflect physical damage onto all his allies, while Mewtwo can only use Reflect, which does not actually reflect damage. While it's pretty hard to compare Psystrike to PK Rockin, Mewtwo is also an exceedingly powerful psychic, and I think it's safe to say that offensively the two have similar abilities.
However, this isn't just about comparing Ness to Mewtwo. In terms of the strongest character canonically, not the overall strongest 1v1 fighter, I believe Ness is the strongest due to a certain event in Earthbound. For those of you whom haven't played Earthbound, in his game, Ness is told to collect the melodies from Eight Sanctuary locations from around Eagleland. He is instructed to collect these melodies and "awaken" himself as the chosen one. Once he collects the Eight Meoldies, he ends up having a relapse of memories of his father, and is ported into a dimension created by his own psychic powers. The realm is created so Ness can experience what influence he has had on this world, and fight his darkest fears away. This realm is called Magicant, and it is created by Ness after he has become awakened by the Eight Sanctuaries in order to ward off his darkest fears, cleanse his traits, and become essentially ridden of all flaws. Once Ness conquers his nightmare, the Eight Sanctuaries bless him and he ties his own power to the Earth itself. He gains a massive boost and becomes the chosen one, ready to fight Giygas with only pure attributes. He has purged all of his fears, greed, and selfishness and replaced it with pure morale and devotion to eradicating the greatest evil of all time, and accepts his fate of potentially never returning back home regardless of the outcome against the embodiment of evil itself; Giygas.
Ness might not have the drive to take over the Earth like Ganondorf, or the speed of Sonic, or perhaps the destructive potential of Mewtwo, but Ness has been purged of all fundamental evils in human nature, and possesses the power to save lives, resurrect the dead and cure otherwise fatal diseases. He may not be invincible, and he may not be a monster of destruction, but Ness is the strongest character in Smash bros to date.
