I don't use Thrive, but Onyx 11 and it takes pretty much whatever filetype you want to give it.
A CMYK PDF or EPS out of Illustrator will usually print just fine for me.
As you should well know though, gradients/transparencies with spot colors will not work correctly. (as in print/cut files)
I have always avoided drop shadows in Illustrator whenever possible as I know they are finicky and do not always result in good prints as the transparency gets flattened in the RIP or when saving the file.
Any other setting you choose besides the basics like color mode as CMYK can result in undesirable results, and are possibly going to be on an individual basis.
ie: One of our Onyx RIPS will really screw up complex radial gradients, while the other hasn't done it so far.... ???
When you are saving out of Illustrator into an EPS/AI file you have the ability to choose your own transparency/flattening settings, even more options are presented when saving out into a PDF file. If you don't know what each of these options mean or what they result in; then choose as little compression as possible, whenever possible.
For raster images:
I have experienced a LOT of wacky things happen from RGB files going through Onyx, and IIRC I have had a couple problems with dropping JPEGs directly into Onyx. I have had the best experience out of CMYK TIFF files, but they are LARGE files.
FYI, 99% of all problems are going to come back to improper file setup or lack of designer know edge/experience and not the RIP messing up the file.