Well, psi IMO is the magic of sci-fi settings. No more, no less.
Having both can be ok for flavour, but having them as actually different things opens a whole can of worms about their interaction, interaction with dispels/wild magic/etc.
Of course the distinction could be only on the power source: spell slots vs psi points. But if psi points work similarly to spell points for the sorcerer, or give extra dice as the bard, you already see that there's no real difference.
The interactions between magic and psionics do need to be codified better, but I think that there would be
less of a problem if there were
more psions in a world. I rarely see psionic powers designed to affect/counter magic, although I wouldn't be surprised if there were at least a few powers that did so. What I mostly see is worry about magic being able to counter/affect psionics (if it can't, psionics is too powerful; if it can, then psionics is just like magic and therefore isn't interesting or needed). If psionics and magic can't counter/affect each other, but there are (roughly) as many psions as there are wizards or spellcasters in general, then I don't think it would matter so much if psionics and magic can't counter/affect each other because there would be more psions to counter/affect psionics, and more spellcasters to counter/affect magic.
The only other really big problem is components, but lets face it, that's mostly handwaved away with spellcasters via foci and component pouches, if not outright ignored altogether, so I can see requiring crystal foci for psionics, or perhaps extended "casting" times for higher-level abilities, to represent the need for meditative focus.
But the concern I actually had is, what is the difference--mechanical, flavor, whatever--between a "Mentalist" psion and an Enchanter wizard? Or between a pyrokinetic psion and a wizard with lots of fire spells and with a hypothetical Pyromancer archetype?
I
also think a lot of the problem is that in media, psychics are typically depicted as specialists: an occultist who channels spirits, an object reader, a telepath/empath who can engage in psychic assaults, a person who can create objects or tulpas out of mental energy, an ergokineticist, a psychic healer, a clairvoyant, an astral traveler. But wizards are more typically depicted as generalists: they can shoot fireballs
and turn you into a frog
and summon monsters
and create illusions
and animate an object to do chores for them.
So do people in general want a psion class that is as versatile as a wizard, or do they want a "realistic" psychic who only has one or two different powers? Or do they want multiple different classes of wizard, like when Illusionist was a class and not an archetype?
I don't know. If I were to have psionics in the game, the type would depend entirely on the setting and genre.