RasIndi - Sorry for the delay and side discussion, but I finally had a chance to look at the files you posted on Dropbox. Thank you for posting them. They were extremely useful. Here's what I found:
a) There is no color space mismatch problem. Because this is a such a common problem, this was my guess before I had access to these files. However, now that I've opened your files, it's clear that both your AI and PSD files are consistently tagged as being in the "Coated FOGRA27" CMYK color space, so there is no problem with this.
b) However, it appears that you made two choices in AI that conspired to make it appear that the problem was in the process of exporting from AI to PS. First, the darkest blacks in your design are clearly "100k blacks" (ie, cmyk = 0,0,0,100), not "Rich blacks" (ie, cmyk = x,x,x,100), where x is usually somewhere between 30 and 70 depending on the cmyk color space).
c) Although I don't have a copy of your AI preferences, from the two images you initially posted in this thread, I am almost positive that you had the
"Appearance of Black - on screen" preference in AI set to
"Display all blacks as Rich Black" instead of
"Display all blacks accurately". As I recall, the first option is the default option for at least the last several versions of AI. This choice made your 100k blacks (which aren't all that black) look like rich blacks when viewing them in AI. However, when exported to PS, they instead were represented in PS as what they really are, ie, a dark gray.
To show that the above two factors are almost certainly your main problem, I changed the AI preferences to
"Display all blacks accurately" (see screenshot below), and then pasted a rich black circle into your document (see 2nd screenshot). The difference in darkness of the blacks between the two areas is now evident. To compete the diagnosis, I then exported this modified version of your document into PS, and, as expected, what one sees in AI is now exactly the same as what one sees in PS.
So, the solution to your problem is simple: Change your AI preferences to
"Display all blacks accurately", and change all the blacks in your design from 100k blacks to rich blacks.
HTH,
Tom M
PS -
MrTom, you were correct: The problem being discussed in this thread is, once again, almost exactly the same problem that reared its head in the thread that you cited. Good call. I couldn't tell this for sure until I had time to open the files the OP posted on Dropbox.