It does depend on the style of music, but it's easy to notice the clash between piano and violin tuning in, say, a slow movement of a Beethoven or Mozart piano concerto. In particular, it's the sharpness of the major third on the piano that can makes a noticeable contrast with what the string players are doing. (string players know all about this, pianists have to put up with it):

(http://www.violinmasterclass.com/en/masterclasses/intonation)

Perfect (absolute) pitch can sometimes be a blessing, sometimes a curse. I don't have it, but my partner did, and she struggled to enjoy some concerts that I enjoyed, simply because the notes from the various players weren't aligned well enough...