Converting that screenshot from the embedded "display" profile to sRGB shows that Photoshop displays correctly. The numbers match.
So whatever the problem is, it's with Illustrator.
The interesting thing is that the swatches in the Illustrator color picker are also right! But the main document color, and the sampling cursor, are both wrong.
If you analyze that wrong blue color further, another interesting thing appears: it's the same color, except the red channel is clipped to 0. It should be 64, not 0! Lift the red channel to 64, and the two colors match perfectly.
I think my prime suspect here would be a GPU bug. Try to disable the GPU (in Illustrator, not Photoshop) and check again. It could also be a defective monitor profile, but for some reason this has more of a GPU feel to it.