Red Ivy is up in Wrigleyville right next to Wrigley Field so there is typically a younger more collegiate crowd there, a little rowdy and fun! Blackfinn is more "upscale", in River North very close to the Loop downtown. I've been to both for the gamewatches, Blackfin food is better, alumni are welcome to bring their kids for the games. The UMAA also typically does raffles for gear at Blackfinn as well.
Both are fun, just depends on your crowd! Cheers, and enjoy your stay in Chicago.