The sensitivity of x-ray radiographic images, meaning the minimal detectable change in the thickness or in the index of refraction of a sample, is directly related to the uncertainty of the measurement method. In the following work, we report on the recent development of quantitative descriptions for the stochastic error of grating-based differential phase contrast imaging (DPCi). Our model includes the noise transfer characteristics of the x-ray detector and the jitter of the phase steps. We find that the noise in DPCi depends strongly on the phase stepping visibility and the sample properties. The results are supported by experimental evidence acquired with our new instrument with a field of view of 50x70 mm(2). Our conclusions provide general guidelines to optimize grating interferometers for specific applications and problems.