Isn't the difference more due to tests levels and announcement precautions ? Pfizer's announced temperature looks like the one for very long term ARN storage while standard fridge for a month doesn't look like it should alter ARN much.
I read in the New York Times article that Moderna and Pfizer use different (proprietary) lipid solutions in the vaccines. It's possible that Pfizer is just being overly cautious and they don't need the ultra cold storage, but it's also possible that Moderna has a fundamentally better solution.
Who knows. Almost all therapeutic rnas have unnatural RNA bases or base linkages that are, for example, resistant to internal phosphatases/autohydrolysis to improve half life; half life can also depend on secondary structure, and of course as a sibling comment mentioned, it can depend on the stability of the lipid nanoparticles.
I'm not sure there's a real difference here.