Touring bikes will have a more relaxed head tube and seat tube angle, longer chainstays, and greater fork trail. The relaxed angles allow for a more upright riding position, and the longer stays and increased trail add to steering stability.
Racing bikes have a steeper seat and head tube angle, putting the rider more directly over the pedals and shifting their position forward. This increases aerodynamic positioning by flattening the back when the rider is in the drops. A shorter wheelbase combined with a steeper head angle and lower amount of trail give the bike quicker steering characteristics (referred to sometimes as "twitchy").

As for which is better for any given situation, that's personal preference.