I prefer psionics to not exist. Or maybe, replace "normal" magic, but I definitely don't want to have both at the same time.
Now see, I quite like having both...and having them distinct/separate "powers/sources." It's become a decent set of plot hooks and setting developments having both Psychics and Mages/Wizards existing in the same world.
1. You get different Psychic "Orders"/organizations that are seeking out psychic individuals and trying to recruit them...and/or end any potential threat the reluctant psychic might/potentially become to their cause.
2. You have different cabals or, if you'll forgive the pun, "schools of thought" among arcane academics about the source and cause of Psychic ability and whence this "innate magic," as the grimoire-toting wizard-types would classify it, stems...How come THEY, masters of arcane spell and occult power, do not possess these amazing displays that require no gesture or incantation? Some hunt down Psychics for study (a fairly universal fear among those with mental abilities). Some seek to cooperate/research in amicable ways -like, "Help me figure out how I can formulate a new spell or potion that does what you do?" Maybe you'll even get paid. Still others simply want to recruit you for another layer of defense (or offense) for their magical/magic-working spaces.
3. You can have different mages (and illusionists) trying to pass themselves off as psychics, by presenting themselves with as many enchantment/mind-effecting magics as they can... and psychics trying to do vice versa.
4. Since everyone knows what a spell-caster looks and acts and sounds like...and druids...and priests/clerics...these guys who make things happen with NONE of that, and no leaves...and no holy symbol...and no spellbook or scroll or wand or anything... clearly, obviously, blatantly, this MUST be possessed by a demon and handled accordingly.
There're a lot of fun scenarios that can present themselves in a world with both spell-casters/"standard" magic-workers and Psychics/psychic powers that are not -or are not understood as- "magic," per se.