Just to be clear here, Travelocity rates Courtyard as 3 Stars, and the Chateau Frontenac as 4 stars, so the rating for the CF is higher. It is reviewers who were more satisfied with the courtyard as a 3 star hotel at a 3 star price, than the CF.

My two cents -

Based on the Courtyard reviews and what has been said on this thread - it sounds like a top-of-the-line mid-level chain hotel. I haven't stayed there.

The Chateau Frontenac is a high-quality four-star hotel, a true landmark. How many hotels do you know that have appeared on more than one postage stamp! It is the place to stay in Quebec. However, it is also an older hotel. Its smallest rooms are not recommended. My wife and I stayed in one of the larger rooms and had a wonderful stay - we took a tour of the hotel, enjoyed sitting in the lobby, absorbing the atmosphere and eating in its restaurant, etc.

I think it depends on what you value. If your only measure is comfort, you will have a fine stay at either location and should probably base your decision solely on price (keeping in mind the aforementioned Fairmont sale). If you are inspired by history and setting, then the Chateau Frontenac is your only choice. The fact that you referred to it as the Fairmont rather than the Chateau Frontenac makes me suspect that history is less important to you in your choice of hotel, but I may be reading too much into your choice of words.