You may only have the dye inks and the original Ultrachrome inks to use since the cartridges are keyed so you can't put the wrong cart into the wrong slot.
About the only thing in common between the x600 the x800 printers and newer are the waste carts and cutters and paper. As far as I know, you can't put an x800 cartridge into an 4000/7600/9600 printer. The only series of printers Epson made that I think all three sizes of printers shared the same ink carts was this series. When they "improved" to the 4800, it took its own special carts that wouldn't fit in the 7800/9800. Same for the x880 and especial for the x900 series. Even the carts for the 4900 are of yet another capacity compared to the 7900/9900 and the 4880 before it.
This is about right according to my recollection. I've worked with almost all of these models.
It's dumb (or profitable) that they made two separate cart form factors for the 4800 versus the larger printers because the carts on offer were the exact same capacity (110 and 220ml carts were available for all x800 series). Seeing a 4800 loaded with 220ml carts was amusing, and they were exactly the same size as the 9800 220ml carts... just keyed differently.
The 7/9900 series changed the form factors completely and all the carts are the same physical size, they just hold different volumes of ink. For the 4900 they had to make the cart smaller to accommodate the smaller form factor.
Interestingly enough the 3880 and 3800 use the same carts except for the Magentas (which are keyed differently). So if you have a friend getting rid of ink on a 3800 and you have a 3880, take it!