The downy is more sparrow-sized, while I think the hairy is more between the size of a cardinal and blue jay, but in this picture you'd use the bill. The hairy's bill is much larger in proportion to its head.
Until I checked, I was so sure that was a great spotted woodpecker (Dendrocopos major). Once you know what to look for, you can easily tell them which one is which. They’re not even in the same genus, but they look deceptively similar anyway.