Which woodpecker is it?

We have a lovely family of woodpeckers (that will not let me get close enough to take a picture !) that visit an old ash tree in our backyard. We learned yesterday that woodpeckers really drum just to make music. They don't have much of a song, so they rely on their beaks to help them make noise. The holes they make are use full to little birds such as sparrows and wrens for homes and nests, not to mention they are a beautiful sight to see as I'm washing dishes and look up into a not so pretty tree and observe two woodpeckers drumming away in the branches.
Now, for identification.
We know it is white breasted with black variegated spots along the wings. It has a red patch above its head. So, that leaves us with two options. One is the downy woodpecker like this:

It is so much like our woodpecker, but notice how it's beak is short. It's beak, if rotated toward its head, it would probably only reach to the end of it's eye.

We have another option. The Hairy Woodpecker like this:

Notice the size of it's beak- if rotated, it would be about the size of it's head.

They look almost identical, but the hairy woodpecker is a bit larger.

So now, we will be on the lookout. We need to see the what the size of the beak is on our woodpecker to know which one it is. Hopefully I can take a picture of it soon to post- until then, we'll keep up our bird watching!