It doesn't matter what colour picker you use. Differences between images in ArtRage and Photoshop are most likely due to colour management. ArtRage does not use colour management profiles, so if you turn off colour management for the document exported from ArtRage when in Photoshop, you should see the same colours.
I'd recommend using PNG due to it being lossless, rather than JPG. However, if you're working between ArtRage and Photoshop then PSD is most likely going to be the format of choice as you do this.