There seems to be a difference between photo printers and fine art giclee printers.
For example, the Epson top of the line giclee printer is the SureColor system which has 6 colors and 4 shades of gray as part of their "UltraChrome" color system and prints at 2,400 x 1,200 dpi with variable size droplets.
Alternatively there is wet process printing which is lasers on photo papers like Kodak Endura. This seems to be currently called "chromogenic printing". Fujifilm has photo printers such as the Frontier DL650 PRO Dry Minilab which are 1200 dpi with 6 colors. (I don't know why they call it "Dry", because as I understand it Frontier is a wet process system.) Another wet machine is the Lightjet, such as the super high end Lightjet 500XL.
The generalization I have heard from printers is that the continuous tone from wet process printers yields a higher effective DPI than ink jet, however, the color rendition is better in ink jet prints than in chromogenic prints.
Is one process better for prints than another, or is it just a tradeoff (like my printer said) between dpi and color, so it is a matter of taste?