I created a certificate of achievement award in Adobe Illustrator and I wanted to save it as a PDF that would have an editable placeholder for the person's name. When I save it as a PDF, the quality/resolution looks terrible on screen, but looks perfect when I print. When I save it as a PNG, it looks great on screen as well, but I can't edit the name.
I'm expanding on my comment, to show you where the settings are.
There is no reason a PDF should look any worse than the original artwork, unless you tell it to. While compression helps keep PDFs small for viewing online and sending them in emails, if you are actually trying to print your PDF it's not recommended.
Adjust these settings, to suit your needs and accounting for where the PDF will be used. If you are using it online, you can typically get away with downsampling a bit. If file size is not an issue (i.e. for printing), then you can turn off the compression all together.
In theory the PDF, since it uses vectors, should look better everywhere, but sometimes there are a lot of little details that some PDF viewers have trouble reproducing well.
Try different PDF viewers - say Preview and Acrobat reader if you're on a mac.
If there's a particular part of it that's not looking good as a PDF, you can try rasterizing (making a pixel image, like a png) just that part. Then you can keep the other parts, like the name you want to change, editable and in a vector format.