No reason to use bags at all for dry trash. As for wet trash, in the country, we compost. In town, between the rats and raccoons, composting really isn't an option, so we do use small garbage bags for the wet trash (and what the vacuum cleaner picks up).
Yeah, when we had dogs, we used poop bags too, no real way around that - I guess you could carry a pail and small shovel on walks and flush the results, but then you're using potable water 
Once something goes into the landfill, it won't degrade regardless. I guess the corn oil based bags are ultimately less toxic - but how much petroleum did it take to grow the corn?
Speed comes from what you put behind you. - Judi Ketteler