Paper bags available around here don't always have handles. As a result, you either can't carry as many (one hand holds a bag from the bottom) or you crumple or tear the bag at the top accidentally. Also, they tend to not hold as much weight as plastic bags.
What's worse is that they're harder to reuse. Since they aren't resistant to water, there are fewer other uses that they are good for.
My paper bags get reused primarily as a place to keep my cans and bottles (we have a refundable deposit where I live) until I have time to take them to the redemption center or give them to one of the local non-profits that collects them. I've found the paper bags allow any residue to evaporate rather than leaving the cans a sticky and, eventually, moldy mess like plastic bags do.
What's worse is that they're harder to reuse. Since they aren't resistant to water, there are fewer other uses that they are good for.