Why do you omit any mention of the color spaces and the Render Intent? (If you convert via Image > Mode then that would all be determined by Edit > Color Settings)
Do you embed the profiles?
Which other applications are you talking about specifically?
If you measure the white regions of the CMYK-image in Photoshop with the Eyedropper Tool what readings do you get?
You need to read up on color spaces, color management and all that stuff. CMYK files will almost always look wrong outside calibrated and managed applications since image viewers or OSX' preview are strictly for RGB encoded imagery....