Advantages of Dye-Sub Printers over Inkjet Printers

Very fast
Relatively maintenance-free
Smooth with no dot patterns visible, even under magnification
Produce excellent shadow detail in dark areas where some inkjets may be "blotchy"
Prints are usually more durable and more waterproof than inkjet prints
For many viewers, dye-sub printers produce photos that look and feel more like real photographs due to the smoothness of the prints and the absence of visible dot patterns

Dye-Sub Printer Disadvantages:
Consumer level models often smear high contrast edges (like a black square on a white background) to some degree, making charts, graphs, and line art look a little less "precise"
Dye-sub prints typically only last as long or slightly longer than a good non-archival inkjet printer and are generally not considered "archival"
Paper type selection is very limited and while dye-sub printers produce excellent glossy photos, most fall behind or do not even offer the option of matte prints
Dye-sub printers use an entire page and an entire page worth of ribbon even to print one small wallet size photo
Pages cannot be normally fed through the printer twice to fill more of the page as they can in inkjets
Dust can sometimes get inside and cause vertical scratches on prints
Dye sub printing and the cost of paper and toner (ribbon) is often higher than inkjet printing