From a public policy perspective, the recent NY plan to tax plastic bags is a one-sided approach to the problem. This is because plastic bags consume less water to produce compared to paper bags. Additionally, some studies indicate that paper bags do not decompose in landfills. Here is a link to a life cycle analysis comparing paper vs. plastic bags. Therefore, any policy that taxes plastic bag use (indirectly) provides incentives for retailers to use paper bags, which when not recycled are not significantly better for the environment.
Most arguments for the use of plastic bags indicate that recycling is environmentally responsible. After discussing this with my friends, I also think that reusing old bags is also a good way to eliminate waste. For example: Today, at the grocery, I asked the cashier not to bag my items because I already had plastic bags in my car. I simply transferred the items to the plastic bags and will continue to have a handful of plastic bags in my car to cover for any contingencies.
Therefore, I think that the argument should not be about paper vs. plastic. Rather, the discussion should be about how we could better reuse and recycle both bags. Let us know in the comments how you plan to reduce your plastic & paper waste.