This is a complex infographic about how the choices you make in selecting a bag affect the environment in a variety of ways.
The data here will show you that, at least according to the calculations by Australian researchers published in Packaging Technology and Science, paper isn't necessarily better than plastic. When they ran the numbers, Helen Lewis, Karli Verghese, and Leanne Fitzpatrick found that paper bags actually fared worse on most measures than even a plastic bag made with unrecycled material.
The best option, given their assumptions and estimates, was actually a reusable plastic PET—that's a type of plastic—bag.
But let me make things even easier for you: Reusing bags of any kind radically increase their efficiency. The more times you use a bag of any type, the better it is for the environment. Of course, some bags are easier to re-use than others, especially the ones built for that purpose. But most plastic and paper bags can also be re-used at least a number of times. And think about it: Every time you do that, you spread the material and energetic cost of making that bag over another trip.
So, in the paper or plastic wars, I think you can find true virtue not just in the material of the bag itself, but in the way that you use it.