I'm terms of real film speed as seen in shadow detail I think slide film pushes better. This was the commonly accepted wisdom at one time though that seems to have changed now. I always had good luck pushing slide film but I was doing my own E6 and got best results increasing development time a bit more than specified.

Provia 400 is a good film but already grainier and contrastier than 400 print films and both will increase with pushing.