Woodpecker

If you measure the spaces on the grid, you could estimate the size of the woodpecker. That would solve this question as the two are different in size.

my guess also Hairy Woodpecker, female.

I would go with the Hairy Woodpecker Picoides villosus - female

Bill size and (vague) black markings on the undertail coverts make this a (female) Downy.

It seems pretty large. Have you considered a Hairy Woodpecker?

I think it is a Downy also. Look on the back of the neck. If there a just a little red then it is a male.

Thanks, I have a hard time telling this species

probably a Downy Woodpecker.......