Creating a Custom Header Image…

I want to create my own custom header (banner with site name, & contact info & logo graphic). Which program is better to use for this purpose- Adobe Illustrator or Photoshop? I have both, but I am a beginner in both.

I tried to make one using Illustrator, and it looked good inside the software, I save it as a web quality JPEG, but when I uploaded it and put it on the blog, the image quality was really distorted. The pixel and the size and the layout and everything I created was good, but as I saved it the image quality turned poor.

So I am wondering if maybe Photoshop is a better program to use for this, or is there a better way to save the header so the image quality is not compromised? Thank you.