The same image with both photoshop and illustrator which are using the same setting and the same profile colour and despite that, colour change a little when pasting from photoshop to illustrator. for example I have an image which the background is yellow with value-c1 m13 y77 k0 in photoshop and when placing it in illustrator these values change a little and I got - c1 m15 y87 k0. Why so?
Did you set the colour settings to same as well?
Check Edit > Color Settings and look what is under Settings. Make sure it's not emulating anything.