On the 9600, 7600, 4000 printers, the carts are all the same and work well from machine-to-machine.
However, there's an ink formulation-cartridge keying that was changed, along with the head between the x000 series and the 9800/7800 and 4800 printers.
From what I understand, you can use the carts between the 7800/9800 but they don't interchange with the 4800 because the 4800 uses non-presurized carts to push the ink but the 9800/7800 do.
Between the x800 and the x880 printers, the only carts you can't use interchangably are the Vivid Magenta/Vivid Light Magenta. All the others are in common. I don't think that you can change between the 9880/7880 and the 4880, though.
Bottom line is that the x600 carts won't work with any of the x800 or x880 printers and vise-versa. Different inks, heads, cartridge keying, etc., and even if you could, you'd need a custom print profile with every combination of ink and remember which was which.
If you want to have the ability to cartridge swap, you'll need to downgrade to an Epson 4000. The 4000 along with the 11880 printer are about the only Epson printers that print Mk or Pk without having to purge the black channel.