Tristana has always been considered a massive hypercarry. She has the largest passive auto attack range in the game at level 18 (pretty sure she even outranges Jinx Rockets and kog'maw, however I think twitch ult still has more range).
Of course with that kind of range, she can't trade auto for auto with a vayne or Kai'sa that needs to be at much closer range. However if you get off 2 autos before they're in range you should win. Also if they stealth/ult into your range, you have W to escape or R to knock them back.
In general Tristana has a better teamfight because she can take down the front line (tanks, divers, assassins) far more easily AND peel for herself in the process. Vayne and Kai'sa both are much better duelists and still strong in teamfights with different forms of safety, but nonetheless they're more likely to get punished for a mistake in a teamfight.