What kind of bird is this?

Your sparrow appears to be a chipping sparrow, clear breast, dark eye stripe below white eye stripe. It is difficult to see the details required for a clearer ID. They are common to your area in summer. I am unable to see the suet feeder bird in the picture.

Visit: www.allaboutbirds.org They have good information on all birds.

Edit: I just re-read the question and realized that you were asking what type of birds would eat the suet. Your winter birds will appreciate the suet, the chickadees, the redpolls. Any woodpeckers will eat suet, or other birds that have the ability to perch like a woodpecker. I find that junco's, other small sparrows have a hard time getting to the suet, although all birds like the fat content.