I had a cooperative Hairy and Downy Woodpecker on the suet log the other day and snapped a few photos. I've learned if you have the opportunity to show them side-by-side you do it. So many people haven't seen them next to each other to get an idea of size comparison.
Hairys have a wide range of length: from 8-12." Downys on the other hand, rarely venture outside the 5.5-6.5" length.
In addition to the overall size of the bird, you can look for these two identifying features:
1) beak length. A Hairy Woodpecker's beak will be nearly the depth of its head. It's very balanced in appearance. On the other hand, the Downy Woodpecker's thin, tiny bill looks small on its face; typically measures half of its head depth. I like to think that the Downy's beak looks like a little ice pick whereas the Hairy's beak is more like a true woodpecker's beak.
2) bars or spots on tail feathers. Here in Minnesota (and the Eastern part of the U.S.), Downy Woodpeckers have black dots on outer white tail feathers; Hairy Woodpeckers have solid white feathers. Oddly, in Newfoundland and in the Pacific Northwest (wouldn't you think they'd be closer geographically?), Hairy Woodpeckers often have the black tail markings of Downy Woodpeckers.