Bluebird vs. The Publican
I don't know anything about Bluebird. (I assume you're indeed referring to Bluebird, the restaurant in Wicker Park, and not Blackbird, the West Loop restaurant that is a sister to the Publican in the Paul Kahan stable.)
I ate at Publican a week or two ago. The savory dishes (meat as well as seafood) were mostly very good. The desserts were just plain awful. It was also incredibly LOUD/NOISY. I'm glad that I tried it, because there were dishes that I liked, particularly the sweetbreads. But I wouldn't go back.
If you decide to go to the Publican, here's a tip. About half the restaurant is communal seating at a very looooong table. When making a reservation, you can specify your preference for the communal or for your own table, and they will try to accommodate your preference but they can't guarantee that they will do so.
Bluebird is a pub in Bucktown on Damen with fair food and a pretty decent beer list. It's also open late which works for us sometimes. Not, in my opinion a destination.
Publican may well be Chicago's most accomplished gastropub. The food IMO is thoughtful, excellently prepared and delightful. The beer offerings way over my head, but the wait staff was great at making recommendations.
I have no recollection of deserts there. What I do know is that when we left, my inclination was to do what the dentist asks me to do -- make my "appointment" for the next time. Right now.
It's hard to get reservations at Publican, which either indicates that a lot of people like it -- or that it happens to be trendy. I suspect that both are true. The trendy part will go away in time.
Publican is probably not a good location for a romantic dinner for two. As nsxtasy notes, the setting is communal and it can get noisy in there, but maybe we were lucky. We sat by ourselves at the end of one of those long tables, had no problems hearing and never felt like we were sharing our conversation or our meal with others.
Other local gastropubs I like a lot are The Bristol (about a mile north of Bluebird on Damen) and Hopleaf in Andersonville. A lot of people also like The Gage on North Michigan Ave. Location is convenient, but I've eaten there three times and was disappointed all three times.
5148 N Clark St, Chicago, IL 60640