Superficially, not much. Both psychic humans and pokémon are largely capable of the same basic abilities: teleportation, telekinesis, telepathy, precognition, and so on and so forth. The difference is in power. While some pokémon possess abilities of seemingly limitless scope and strength, humans are by and large hindered by their own psycho-physiological makeup. For this reason, the strongest human psychics really only possess abilities that are on par with the likes of mime jr., smoochum, and other relatively weaker psychic-types in terms of strength. The only exception (who’s been recorded, anyway) is Sabrina of Saffron City, but even Sabrina admits she’s uniquely powerful.
More importantly, though: pokémon as a whole possess a unique trait that sets them apart from any other living being on the planet, and that is their ability to organize their respective elements into special, identifiable techniques we humans know as moves. This is also why, no matter how incredibly strong humans can be, they can’t execute normal- or fighting-type moves. We just don’t have the capacity for translating our efforts into consistent maneuvers like that. So although both humans and gardevoir or alakazam or so forth are capable of using telekinesis, we are not capable of controlling our telekinesis with the consistent strength and precision needed to execute Psychic.
In other words, one could say that although we may be powerful in our own rights, humans are slightly weaker and certainly more primitive than pokémon when it comes to channeling and controlling the elements.
The Pokédex According to Bill 