In the same way that we non-pianists don't all play the same way, pianists also don't all play the same way either! When finding the appropriate pianist for your piece, recital, competition, or jury, it's important to review the type of music you're playing and what kind of musician you are (solo or chamber?) so that you can find the best pianist to match your style of playing.
When your style of playing doesn't match, it shows. One musician will overshadow the other, or one musician expects the other to respond musically as an equal but doesn't receive the response they're expecting... It can be disastrous on stage.
But if you guys do match, MAGIC HAPPENS. I had one friend who described my performing a trio with a pianist and oboist (at the oboist's graduation recital!) as "jedi mastery". She asked us how we did it, how we could "read" each other without even looking at each other! The simple answer is that all 3 of us connected. We became 3 working members of the same body, so we could read each other's queues in the same way that if you feel an itch on your ear, your hand will naturally gravitate upwards to scratch it.
So go forth and find your piano soulmate! Make magic happen! :D