When you go to "Save as" and then select .jpeg, you should get an option of what quality setting you're saving it to. It might be automatically bringing down the quality level. I believe the setting is out of 12, but you'll only notice a big difference when it gets to 7/8 or below.
Are you saving at 12/12?
You might be able to see what you get saving at .png-24, it might be better for you.
Also, if you select "Save for web" you will notice some color changes and usually lesser quality, perhaps that is what you're referring to?