No, I wouldn't feed them the poor quality. If all you can get is the better quality, then that will be okay, you'll just have to be more careful and watch them to ensure they aren't getting too much and risking colic or founder.
The new hay that you're getting, what kind is it and do you have any idea on the nutrient content?
I've seen grass hays that had more nutrients than most alfalfa and I've seen alfalfa that had fewer nutrients than most grasses.
Just starting them off from a starved situation, the first few days I'd likely want something that wasn't much more than 10% protein, then gradually increase it over the next few days to between 15% and 18%.