Dunno why. Which versions of ID/AI? Not that it should matter, I get the same results with CS6 and CC2014.
One square in ID is native, the other from a placed AI file--though drag and drop are the same results.
Acrobat, hovering over one square...
And over the other square...
I used your hex values in Illy, used Illy's CMYK values in ID.
I see a difference between those colors. You can't tell when there's a different colored border between the two, but when you have the two perfectly side-by-side, you can very faintly tell that they are different colors.
I'm using CC2014 for both applications.
Can you upload a sample that demonstrates the issue? Sample AI, sample ID, ZIP them up, upload to dropbox.com or the like and provide a download link.
The numbers in Acrobat are the same in my sample. So assuming your color numbers are the same, the same working spaces, without seeing/checking a difference in a sample you provide I don't know what to suggest.
The InDesign document is also set to CMYK and is using the SWOP v2 color space
InDesign doesn't have a document color space, you can have a mix of Lab, RGB, and CMYK colors on a page. Don't spec your InDesign color as a hex value, get the actual CMYK values from the logo in Illustrator and use those values to make an InDesign swatch in the Swatches panel. If you use the Color Picker be aware that when you pick color there the mode can be RGB, Lab, or CMYK—make sure you are making a CMYK color.
I knew it was something dumb I was doing wrong. Of course I shouldn't be using hex values in CMYK mode - hex is just another representation of RGB.
The colors were different but InDesign sure didn't make it easy to tell. Selecting the InDesign shape I made and pulling open the color menu revealed that the Cyan value was 46, but dragging the color picker tool showed Cyan 45. Dragging the color picker over the Illustrator logo, meanwhile, showed 46. Problem was solved by entering new color values into both the InDesign document and Illustrator document using CMYK values, instead of hex values.
Thanks for pointing that out. I feel silly but at least my document isn't having serious clashing issues anymore...
Of course I shouldn't be using hex values in CMYK mode
It wouldn't be impossible to get matching colors when you define hex, both programs make color managed conversions of hex colors to CMYK. To get a match all of the document color settings have to be the same—the source RGB as well as the destination CMYK profile and the Conversion Options (Intent and Black Point Compensation). Illustrator uses the Color Settings' Working RGB profile as the source, but InDesign doucuments can have an assigned RGB profile, so it uses the document's assigned RGB profile as the source.
If you were to sync your Color Settings to North American General Purpose, which is what Mike probably did, and make new documents in both apps, your #86c8cf hex color should produce the same CMYK values.