I did a little research, and wow is this complicated!!
Most paper bags are 40-75% virgin pulp and 25-60% recycled paper (according to the American Forest and Paper Association). Virgin pulp is needed for strength and elasticity. Plastic bags are also primarily made from virgin material, for strength.
Plastic bag are more effective to make- their raw material yield is more than 90%, compared to paper bags 75%.
Manufacturing plastic bags releases 92% fewer emissions into the air than manufacturing paper bags.
HOWEVER, shoppers tend to use 3-4 plastic bags for every 1 paper bag. And about 45% of paper bags are recycled, compared to 5% of plastic bags.
When I forget my cloth bags, I use both- and then reuse plastic for little trash cans, and paper for sending packages (rather than buying the brown paper rolls).
(Stats from deliciouslivingmag.com/greenliving/dl_article_222/, which had a lot of other good info, including that since paper bags are biodegradable, "gardeners can throw garden clippings into a paper bag, then put the whole package into a composting bin, which hastens the breakdown of the bags.")
Whole Foods has gotten ridden of plastic bags, and their paper bags are 100% recycled paper, 40% post-consumer. That's pretty good, so I guess if you aren't reusing your bag, maybe you should shop there? :)