No one in the modern prepress industry wants to work with EPS anymore. It's an almost obsolete file format. Here's good information found online. Most of which I already knew, but saves me the time or writing it:
Here are the major issues with EPS.
(1) EPS doesn't support ICC Color Management. Everything is either DeviceCMYK, DeviceGray, or DeviceRGB.
(2) EPS doesn't support live transparency. All content with live transparency, including clipped images, must be flattened potentially causing text and vector objects involved with transparency to be rasterized at some resolution which probably won't match the resolution of your output device (which you probably know at the time of content creation anyway). If text and vector overlap with transparency, text may be converted to outlines. Text in the resultant PDF will not be fully searchable or be able to be “touched-up” due to this flattening process. And the text won't render at highest quality!
(3) The results of (1) and (2) are device resolution and color space dependent files with the possibility of terrible artifacts when either displaying or printing. There is no recovery from this!
(4) PDF is much more compact and compressed than EPS, but with potentially higher fidelity.
(5) There are no good tools for displaying EPS. PDF is ubiquitous for display and print. Adobe Reader is free!
Note however, that if one is generating PDF for any type of content, a parallel file should be maintained in the file's native format. In other words, if a vector diagram is created in Illustrator, save the file as an Illustrator file and save a copy as a PDF/X-4 file!
Heck, even though printed material is CMYK (plus some possible spot colors), a lot of users don't even work with CMYK images anymore. Or more precisely, the advertising agencies who put together brochures, flyers, catalogues, etc. only use their RGB photos when building their InDesign or Quark documents, and let their vendor do the CMYK conversions on their RIPs. Then they only have to track one master image that can be used both on their web site and for print.
An Illustrator PDF isn't actually even a PDF. It's still a native .ai file with a .pdf extension. This started somewhere around Illustrator version 12 (called CS2). Go ahead, take any PDF and change the extension to .ai. It will then open in Illustrator as if were always an Illustrator file. Same thing in the other direction. Take any .ai file made from about CS2 of Illustrator forward and change the extension to .pdf. It will then open in Acrobat, Preview, etc. as if it were always a PDF.
In short, forget EPS. It's basically dead. Use an action in Illustrator to run all of your EPS files automatically to a PDF.