Quoted Creamsoda "if you're a heavier guy / harder hitting rider, go for 31.8, but if you want to save weight and/or don't mind (or want) the flex, go for 25.4. it's beneficial for street bikes (esp. rigid ones) to run 25.4 because the flex helps absorb landings just like how steel frames do (vs. aluminum frames)."
Basically the main reason you see dirt riders running 31.8 and street and park running 24.4 or 22.2 .
Here's an old post courtesy of Eric at Deity that I think answers the question perfectly;
"You know, the biggest misconception between 31.8 and 25.4 Handlebars is that 31.8 is stronger. There is no strength advantage to a 31.8 Handlebar over a 25.4, but what you do gain is stiffness. The oversized 31.8 bore (no matter what material) will be stiffer than a 25.4, but this lends issues also to consider.
For example: hand fatigue, inability to cut bars down as much as a 25.4, and lastly 31.8 bars will weigh a little more due to the extra material necessary for the larger bore size.
It all comes down to preference and most street bikes would benefit from 25.4 kits, but if you are looking for pure stiffness out of corners, sprints, descents the whole nine...you cannot beat the 31.8s.