Illustrator or Photoshop to JPEG, what's best?

I have to make some designs for print. I know that Illustrator or InDesign are probably better if you’re designing for print, because they handle fonts and vector images better. But that’s when you actually print IN Illustrator or InDesign. What about when you have to export to a JPEG?

I HAVE to deliver the end result in JPEG’s. I’m used to working in Photoshop. My question is: does it have disadvantages when it comes to quality of the image?

I think if I export to a JPEG, it doesn’t really matter whether I use Photoshop or Illustrator or InDesign. Does it? Keep in mind, the JPEG’s are meant for print.