If you look at the Seiko Presage enamel dials, there is a tremendous amount of discoloration and surface defect visible anywhere hands, date, or a complication indicator places a hole in the dial.
Second, cheap enamel can be executed on copper or silver, but the best examples use a gold dial base plate as a starting point.
Third, how many layers are applied and how well they are fired can influence the richness and smoothness of the dial. Great enamel can have up to 20 layers even if the dial is just a solid color.
Fourth, surface smoothness is difficult to achieve with enamel, and that's why the vast majority of enamel dials are white; it hides defects. That's also the reason that even Patek Philippe enamel dials avoided dark colors until the last decade. For years, even flagship complications like the 5016 would receive lacquer dials if black dial color was requested. Flawless black or dark blue enamel is a sign of excellence.
Fifth, are the graphical features of the dial applied after the firing or an integral part of the enamel itself? The best enamel dials are all-enamel, and cheaper enamel dials have tampon-applied numerals, indices, etc. like a regular watch dial.
Sixth, any combination with cloisonne, champleve, engraving (e.g., Patek 5738/51G), paillone, or miniature painting raises the challenge and skill level required at a geometric rate. Flinque enamel involves applying a layer of translucent enamel over a guilloche or engraved base, so the see-though enamel layer must be optically clear and flawless in order to avoid obstructing or distorting the view of the cut dial base.
I'm sure more will come to me, but this is what I can recall of the top of my head.