The ratio in pressure between the two flasks will be the same. But the absolute amount of rise or fall in pressure within each flask will not be the same.
It's basically a simple linear equation, y = mx + b. If you have two lines at two different slopes (assuming same intercept), then at any given x the ratio of y between the two lines will remain the same, but obviously one would rise/fall faster than the other. Here (m/M) is the slope aka derivative or rate of change.
But in general I would agree with you guys that if there's liquid water -- due to condensation or sloppiness -- then that would be the dominant factor, barring extreme temperature & humidity conditions.