Here's two side-by-side same-resolution ceramic samples where one clearly shows the print process, and another doesn't.
The first is a sample Chipco Oyster (25c...who needs those! - heh)
The second is a VERY dirty Casino Arizona $5 chip I found laying around.
On the other hand, the print on the Paulson $5 "UFC 100" chip from Mandalay isn't so much showing a resolution issue, so much as it's showing that it's from a 4-color print process, and that it has to use CYMK (or similar, that looks like CYMK to me) to do whatever they're doing in print.
I assure you, that chip look STUNNING when it's not under the microscope. Being able to zoom in and see the print process isn't exactly how you tell if a chip is good.
If you're doing vector graphics in CYMK or RGB or Panatone, you probably want to match them to what your printer can do. These are the subtleties of custom printing.
A shame. Presumably you could contract a "better" process-matching printer for any non-ceramic chip that you do -- in that you're just putting your own sticker on them. I wonder if I've got an ASM or Blue Chip sample anywhere in the house.
So, anyway, different chip-makers use different print processes. Pick a chip-maker that can print what you want (pictures, graphics) and have it look good on the medium you've chosen (paper, vinyl, ceramic, etc.).
Now if you'll excuse me, I have go to finish gaining the Dwarves' support for fighting the Darkspawn...