For quality - I'd say BR. I've never really shopped at Club Monaco so I couldn't really tell you what their quality is like. Zara is probably the lowest in terms of quality however, I do like their designs.
I guess it really depends on what you're looking for stylewise. BR is fairly conservative/business like. Zara and Mexx is a little more adventurous with some "out there" designs on some of their clothes. Club Monaco probably sits right in between BR and Zara/Mexx but I've noticed is really suited for the skinny people.
If for overal popularity (as in brand recognition), I'd say BR takes the cake. Everyone knows what BR is anywhere in North America.