A Cooper's Hawk is roughly the size of an American Crow while the Red-tailed Hawk is considerably larger. We've had two Cooper's Hawks, an adult and an immature, visiting our West Toledo backyard this winter, harassing the songbirds and occasionally snagging a Mourning Dove. Cooper's Hawks mostly eat other birds while Red-tailed Hawks mostly eat small mammals. But they both cross over to other food types depending upon the season and when an easy opportunity exists.
Since MaumeeMom's bird was chowing on rabbit, it was probably the Red-tailed Hawk, unless it was a tiny rabbit. I would think an adult rabbit would be too large for a Cooper's Hawk. Anyway, it's cool to see life in the food chain, nature that is, even if a cute animal gets shredded. Raptors need to eat too.
I saw a Red-tailed Hawk in our backyard a couple times last month, which is a bit unusual. Cooper's Hawks are more likely in an urban setting, especially if bird feeders are attracting little birds. These raptors are probably migrants that are hanging around for the winter and will head north when spring arrives. We have one or two Cooper's Hawks visiting our yard each fall and winter, but they disappear in the spring.
Like transcom said, the big birds you see right now along the highways and country roads, perched on lampposts, road signs, guardrails, telephone poles, and trees are typically Red-tailed Hawks. The adults will have the reddish or rust-colored tail. The belly-band on the Red-tailed Hawk is dark on some birds and faint on others.
Sometimes you'll see a small bird, hovering low along the side of the highway or in the median, even around the I-75/475 split in Toledo. That's the American Kestrel, which is a small falcon. When driving around our countryside, the Red-tailed Hawks will perch on the poles while the American Kestrels will perch on the wires.
Now if you're really lucky, you may see a Rough-legged Hawk in Lucas or Ottawa county. This is a northern raptor that's visiting us for the winter. A few are around right now. Rough-legged Hawks come in two different colors or morphs: dark and light. And they're slightly bigger than Red-tailed Hawks. Sometimes they perch at the top of tiny trees or bushes that appear too small to hold such a large bird. Drive around just south of Rt 2 a little east of Toledo, and you may see a Rough-legged Hawk.