We actually had an issue, so I did a lot of googling on it.
Basically Adobe themselves said Eps is dead, and to move onto pdf.
Illustrator is either transparency on, or off... For basic stuff it works .For stuff like shadows, or anything "fancy" if you don't flatten it, you're going to lose the transparency.
Most on here have to remember, I do go from the embroidery world. Shadows and the "fancy" effects don't translate well into embroidery. Even if digitized flawlessly, due to how one "breaks" down the shapes for production.
I tried switching to pdf, it lasted until my first file setup. I know it's a bad habit... But we do lots of real estate signs / arrows, a customer will order for their whole shop... 10 different names / designs, x 2 different arrows... So 20 different images. Most of my designing is from layers... I know, I probably should use artboards.. but I was self taught, and it was just a habit. Pdf won't save anything not on an artboard..
I use layers a lot as well. Not so much artboards, for my workflow that's actually more of a detriment then a help.
However, the killer thing is that the digitizing software that I have (commercial software anyway), don't accept PDFs directly. Have to use some intermediary program (in Wilcom's case, that's DRAW, unless your like me and don't install DRAW and use Ai). It will, however, read EPS (and it will translate the transparencies of said EPS file as well) directly. Not bad for programs that refuse to "grow up" and be 64bit (that would be the embroidery programs, not EPS "programs" that some people seem to think I'm talking about, no not you ikarasu).
Also, PDFs do actually save beyond the artboard, they just don't tend to display beyond the artboard. If you bring that PDF back into Ai, you should still be able to get the entire graphic. At least, I've been able to. Just actually had to deal with that for a client yesterday as a matter of fact.
One of the head guys at Adobe actually came out and told everyone eps is dead, and move onto pdf in their forums. He had a big post on all the stuff pdf can do, that EPs doesn't, such as save input ICC profiles.
In my world, that's not as a big deal as it is in y'alls. Just like Ai's artboard limitation isn't that big of a deal for me.
You should at least at home have a pirated illustrator to be able to convert artworks. It's not very professional rejecting a client with AI file extension.
Personally, I find it more unprofessional to have a pirated copy of programs that people are expected to buy for a particular business (or use programs that they can get legit without paying if a budget is that tight).
I'll reject files regardless if it's vector or raster if the design cannot be reproduced cleanly in my production method of choice or if there are other things wrong with it (fonts not outlined, linked files that are sent along, embedded design not actually vector but a low res raster file etc).