Absolutely not true. For mainstream usage and single threaded applications, there will be virtually no appreciable difference. Of course if you are running more intensive programs that utilize the superior quad-core processors then the difference will be much greater. But to imply that the 13" feels dated is simply not true at all, especially since both machines share the same PCI SSD.
I agree for most of what you stated there; however I must point out that there seems to be a general lag when it comes to scrolling and UI animations. I assume the Iris 5100 is largely to blame here, as it doesn't have the fast eDRAM cache of the Iris Pro 5200.
For instance, opening Mission Control and Launchpad. The frames seem a little jerky when opening these.
Performance wise for the average consumer, there mightn't be any noticeable difference but when it comes to user experience, the slight jerkiness of the 13" sort of disappoints my experience.