I have seen Nick's get very crowded during the week (seems like a lot of larger groups and expense account meals) but the food has always been very good. For price, think the Morton's Stekhouse range. I think you can eat in the bar area as well on a first-come basis, which may be a bit faster. Never done so myself.
Harry Caray's is a lively atmosphere. There, I have only ever eaten in the bar area (wow was it crowded when the White Sox were playing). Good size menu, a variety of beers and wine, though not as upscale as Nick's. They do offer a bunch of steaks and chops, as well as a bunch of different big dinner salads. Food has been consistently good.
The two are within a stone's throw of eachother. Enjoy whichever way you go.