I regularly compost. Currently I strictly use straw as bedding, but also have lots of wood chips for various projects. In my experience, straw breaks down considerably faster than wood chips. Of course, this does require frequent turning. I turn my compost piles about once every 3 weeks (I do have a 'slow compost' bin that never gets turned, and which I harvest once a year).
Straw does take a long time to decompose and therefore (as another poster noted) is used to retard soil erosion. In fact, I add straw to my garden in the Fall before tilling it to help break up the soil (I have high levels of silt) so the roots of Spring plants can penetrate better. However, straw in the soil is not the same thing as straw in a compost pile. The heat produced in the later does quickly (by comparison) break it down.