Yes, stone will last longer, simply because it doesn't get eroded by the elements as quickly as possible. But it's also simply not usable as a construction material for bridges beyond a certain size and span, because it's only good under compression and even then its own weight starts to become a limiting factor as you get larger.
By the 1940s, a stone bridge that might take 100 man-years of labor to create could be replaced by a bailey bridge that goes into place overnight. I'm sure if we wanted to create a bridge that lasts 300 years, we could dedicate more resources to it, but it would be grossly wasteful to do so - you don't know how long the current requirements are going to even be relevant. It's better to build a bridge that lasts for 50-60 years, and have the option value of replacing it with a better structure down the road.