The version 2 is also popular among electrical engineers as the variable $\xi$ is then the actual frequency. For an electrical engineering view on the Fourier transform, I can recommend the lecture notes The Fourier Transform and its Applications by Brad Osgood.
One downside of this convention is that the handy rule of differentiation gets a bit more complicated (namely $\hat{f'}(\xi) = 2\pi i\xi \hat f(\xi)$ instead of $\hat{f'}(\xi) = i\xi\hat f(\xi)$).