One is metal-free with no grey gum line; the other is cheaper and still valid in specific cases. Here is when each one wins.
Metal-ceramic crowns have a metal substructure covered by porcelain. Over years the gum recedes a fraction of a millimetre and the metal edge shows as a dark line at the neck of the tooth. Monolithic zirconium has no metal at all, so that line can never appear.
In a metal-ceramic crown the porcelain is layered on top of the metal, and layered porcelain chips — most often on the biting edge of upper front teeth. Monolithic zirconium is milled from one solid block, so there is no layer to break away.
Very long bridges spanning many missing teeth still benefit from the tensile strength of a metal frame, and the price difference matters when you are restoring a full mouth on a tight budget. A good dentist will tell you when this is the case rather than upselling by default.
For single crowns, front teeth and full smile designs we use monolithic zirconium as standard: better light transmission, no chipping layer, no grey line, and a 15–20 year service life. That is why it is our default rather than an upgrade.
Modern multi-layer zirconia has translucency close to enamel. The unnatural look people fear comes from over-white shades and identical shapes, not from the material.