My supermarket in France uses biodegradable bags for the serve yourself vegetables. I tie the knot carefully and reuse them in my food waste bin in the UK. It goes for anaerobic digestion.
Does it make much difference if the bag is going into land fill? I do not know. I reuse old plastic carrier bags for my waste bin, I do not buy special ones. If I was going to throw a bag away without using it, I would prefer a compostable bag because I can do just that, put it on the compost heap rather than in the bin.