The biggest advantage the dyes had, was on gloss type papers.(more closely mimicking traditional photo prints) While you can print dyes on any of the micro-porous papers aimed at pigments, fading can start in just a matter of months. The micro-porous surface opens the inks to atmospheric contaminants--primarily Ozone, that breaks down the dyes quite quickly. The preferred papers for dyes are coated with swellable polymer, that incapsulates the droplets. These were mostly made by Ilford, under their "classic" label. Dyes can last a long time under low humidity conditions.
The other major advantage of dyes over pigments is the lack of residue build-up in printers and keeping all nozzles firing. They require much less maintenance. But modern pigmented printers have been improved over the last 5 years to greatly reduce these problems.
But, as Ernst has stated, the new crop of pigmented printers has for the most part resulted in prints that are look nearly as good, that can be printed on a very wide array of papers, and last easily a 100 years under average viewing conditions.