I don’t think there actually is much of a disparity between the games and the anime – obviously the anime depicts them, mostly, as being of human or near-human (or, in a few cases, super-human) intelligence while the games generally do not, but I don’t think the games so much contradict the anime as fail to support it. You are right, of course, that Pokémon don’t have much of a personality in the games – but wouldn’t we be playing a completely different game if they did? It’d be a great deal of work to give actual personalities to individual Pokémon, and at the end it would be all but impossible to keep the collecting/training/breeding game structure that’s worked for the franchise since the beginning, so why bother? And, of course, we still do have Pokémon that are explicitly described in the games as being highly intelligent, such as Alakazam with his ‘IQ of 5000’ (which, incidentally, is an utterly meaningless statement because the IQ scale just plain stops making sense once you get to maybe 190 or 200), or even Pokémon capable of human speech (the ghost of the mother Marowak in Lavender Town).
In short, what I’m suggesting is that Pokémon don’t appear to lack personalities in the games because the games take a dimmer view of their intelligence than the anime does; they appear to lack personalities because the games just don’t care. When people do talk, in the games, about the intelligence or personalities of Pokémon, they tend to say things along the lines of “just like people!”, and the relationship between humans and Pokémon has always been portrayed as an equal partnership, implying that they are at least of comparable intelligence – quite a bit brighter than a standard cat or dog.
The other thing to bear in mind is that ‘intelligence’ is a frightfully nebulous concept anyway, and that most psychologists would be hard-pressed to pin down what it actually is. I am actually tempted to suggest that Pokémon are, broadly speaking, quite close to humans (or, in some cases, well above them) in their capacity for logic or ability to guess future events, but fall behind mainly in areas like leadership and creativity, which is what trainers are expected to provide. But now I’m speculating.
