That's not as simple an answer as you might expect because it "just depends".
AI is the native format of Adobe Illustrator. It contains the contents of the page or workspace along with things like page size information. An AI file is written in the Postscript Page Description language. EPS stands for Encapsulated Postscript. It is also written in the postscript language and typically does not include page information but does add both a low resolution preview and what is termed a placeable header which is needed for applications like Adobe InDesign, Quark Express and Pagemaker.
If you save as EPS from Adobe Illustrator, the above is what happens. The page contents remain unchanged be they vectors or bitmaps. In actual use there is very little difference between using an AI and an Illustrator EPS file.
Where it gets complicated is that many applications can open or save an EPS file but it may not be as universally readable or unaltered as what will be saved from Adobe Illustrator. Programs such as CorelDRAW, FlexiSign, SignLab, Gerber Omega, etc. will all open or save both EPS and AI files. But each will do so in its own flavor. Several will fail at opening their own saved EPS files. Then to further complicate the issue, one can also save an EPS file from Photoshop even though the contents are normally all bitmapped images and no vectors. Great for color management (one of the things Postscript is used for) but useless for vinyl cutting.
So it just depends ...