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Looking at various site's nav bars I see some sites spread their content wide across the bar, anchoring their logo to the far left and login to the far right, navigation in the middle (examples: squarespace, medium). And some sites align nav bar content to the main content grid (examples: campaign monitor, ny times).
Are there reasons why one way is preferred over the other?
I can't find any information on which is best for usability on a responsive site.
One way is not preferred over the other. If that was the case, we would see majority of sites using one approach. I prefer design 1 over design 2 and it is just personal preference. There is no substantial advantage or disadvantage with either design. Comes down to individual choice. I cannot think of a business requirement that makes a strong case for one design over other. Again I am talking only about the two examples you posted.
