Both use 8 separate Durabrite ink tanks and the main difference seems to be the colours used in printing:
Epson Stylus Photo R1800 Printer
Cyan, Magenta, Yellow, Red, Blue, Photo Black, Matte Black, Gloss Optimizer
Epson Stylus Photo R2400 Printer
Light Light Black, Light Cyan, Light Magenta, Light Black, Cyan, Magenta, Yellow, Photo Black or Matte Black
The R1800 is also slightly faster.
The results will presumably be slightly different because of this (I have not seen prints from the R1800) and it will be a matter of personal taste as to which each person prefers.
Some companies used to supply sample prints from your own photographs. I do not remember who they were but other members may be able to help with that.
R1800 click here
R2400 click here
The R800 seems to be similar to the R1800 but only prints to A4.