If you look at the colour settings there are subtle differences between applications. Now if I could see your settings then it would be less abstract to discuss what and why.
For one Illustrator has "preserve numbers" as a CMYK option, which does not appear in Photoshop.
Why? Well lets look at what the software is intended for and the problems that can occur. Photoshop is for editing, compositing (creating) mainly photographic images, in these images when you convert from RGB to CMYK you want to preserve the appearance of the image. Colour rendering is key, and black as K only is not really relevant. If you ask a printer photographs are easier to print. There are some special cases that will produce problems in Photoshop, converting and printing Screen dumps is one of those issues, and you can se many books (even great photoshop manuals) that struggle in giving good screen dumps. How to get crisp texts, and greys that are consistent. GCR can help some, but there are tough decisions on how to handle a RGB grey and RGB black (smoothness vs stable neutrals)
(When thinking of RGB think of why a tripod has 3 legs and not 4 (CMYK)… it's more stable! If it had 4 legs it would wobble).
Now letts consider Illustrator. Illustrator can be used for so many different types of creative work, but lets consider a technical drawing. If you have text and line art you (your printer) would not want 4 colour conversions of fine lines or text… it would be blurred and a small stretch of paper in the printing process (that is in the natural world with living materials affected by temperature and humidity and a myriad of other factors). Now this is why there is the "preserve numbers" option in Illustrator, involuntary CMYK conversions will ruin any technical documents. Also you want to be careful of involuntary conversions of other colours like yellow getting dashes of Cyan or black. You need to look at a job and decide is it clarity that needs to be preserved or exact colour match? Automatic ICC conversions is a bit like one-size-fits-all solutions, and synchronising settings is like giving kindergarden kids XXL T-shirts because then you can combine it with the order for the teachers… it may work in some cases (like if you are looking for a one size for all knitted scarves), but if you are wanting to handle multiple inputs and/or multiple outputs better to know what is happening.
It is possible to get Illustrator and Photoshop to convert colours in the same way, they do use the same colour engine, but it does require setting up each program correctly, and here you would need to look at the colour settings in advanced mode to spot the differences. But as I say I do NOT recommend going by synchronising the settings.
What makes it difficult to know how to get into a discussion is there is so much pre-required knowledge and hard to get a feel for at what level to start and to what level to discuss. I would love for the Adobe Bridge to, instead of having a "Synchronise all" dialogue to have a flow chart explaining the different workflows and what colour management route to go by. As Einstein said "Make things as siple as possible, and no simpler than that" in my opinion "synchronise all" is making things too simple, and causing confusion (and dissapointment) as a side effect.
