Brookfield is much larger. It's also out in the suburbs, so it's a bit out of the way. There are some really good exhibits at Brookfield. Wolf Woods is top notch. Habitat Africa is also pretty outstanding. You'd also get to see the ever-controversial Tropic World.
Lincoln Park is free and closer to Wrigley Field. Expect to pay a lot for parking. Their gorilla/chimp exhibits are very, very good. African Journey is another nice one with a decent collection of species in both indoor and outdoor settings. There are some ancient buildings such as the Kovler Lion House that aren't much to look at unless you're into really old zoo architecture. The Brach Primate House isn't much better.
If it were me, I'd hit Lincoln Park and some downtown attractions. Battling Chicago traffic to get out to the west suburbs will likely be an all day event. I've seen Lincoln Park, the Shedd Aquarium (honestly more of a must-see than either zoo), and the Field Museum in one day. I'm a fast walker, but it's doable.
IMO, the top two animal enthusiast attractions in Chicago are the Shedd and the Field. Getting Lincoln Park in with them for free is just the icing on the cake, and far less of an adventure when it comes to getting around.