Yes. Gradients in particular have a tendency to start 'banding' when moved between different vector packages -- I used to get it all the time moving files between Freehand, CorelDraw and Illustrator, even when saved as EPS files rather than any of the proprietary file formats.Watch out for trasparency and gradietns but for flat art you'l be fine.
we use both corel and ai at my job, and i haven't been able to get corel to open ai..? maybe its a function I'm missingAFAIK Corel opens .ai as well as .eps files. I run into the same problem with every printer here using Corel exclusively. Never had a problem with the print output yet though, I give them .eps's and print ready PDFs of the same file.
If you place a JPEG in an AI file and save or export as EPS you will not have vector art in the EPS....
the current format i have it in is jpeg. but i can easily transfer it to eps/vector cause i do have illustrator.
The T-Shirt question from @krossfyter is about 6 years old!The T-shirt company might accept an EPS, but they may be really limited to CDR format files. You need to find out what elements you can include in the CDR file. They may need pure vector or may accept placed bitmaps. You need to find out. You also need to find out whether they require either CMYK or RGB color space and whether they accept, or even require, spot colors.
Making a new thread would have been easier to read through the topic. Nevertheless I try to answer your question.... here a small crash course..I sent a PDF front and back, but they responded (a week later) telling me I sent two images and they didn't know what to do or what size to print them at. Then they told me they wanted CDR files.