IMO Photoshop EPS support is not the best. If you have vector layers in your document like text layers and save the document as an EPS file when you open the EPS file in Photoshop it will open as a single pixel layer the opened document will have no vector layers just a single pixel Layer. If you want to be able to edit you document in CC save you document as a PSD or PSB file with max compatibility option. Photoshop also supports layered Tiff file most applications will however ignore the layers in a layered tiff and just use the tiff composite layer. So I never save layered Tiff files.
Going from old to new is never an issue.
The other direction could be, if the file has properties not supported in the older application version.
Don't even think about eps. That format has its (limited) uses, but this isn't one of them.
I always save at least one version as PSD (the native Photoshop file type).
EPS isn't something I've used for many years.
I sometimes come across EPS for small vector logos, where PDF feels a bit like overkill. It's still used as vector interchange format in the printing industry.
Anyway, this is going a bit off-topic. David, save as PSD or TIFF, and anything you save out in CS6 can be opened in any later Photoshop version, present or future.
Going the other way, check "maximize compatibility" in PS preferences. This includes a composite flattened layer that previous versions can read, in case there are elements in the file that were invented later.