The quick answer
Choose Tadelakt if you want a warm, hand-made, organic finish with soft movement and are drawn to natural, earthy tones. Choose microcement if you want a precise, uniform, contemporary surface in almost any color. Both are seamless and both can be waterproofed for showers.
What each one is made of
Tadelakt is a Moroccan lime plaster, burnished with stone and sealed with natural soap. It is a centuries-old craft and it looks it, in the best way: slightly undulating, soft and alive. Microcement is a modern cement-and-polymer coating, pigmented and sealed, with a flatter, more consistent surface.
Look and feel
Tadelakt has depth and gentle variation, a bit like polished stone or old plaster. Microcement is more even and architectural, closer to a fine concrete. In a warm, natural bathroom Tadelakt feels right; in a sharp, modern one microcement often does.
Waterproofing and care
Tadelakt is waterproofed by the burnishing and soap process itself and needs periodic re-soaping. Microcement is waterproofed with sealers and needs periodic resealing. Both are grout-free, so both are easy to keep clean; neither is truly maintenance-free.
Cost
Tadelakt is usually the more expensive of the two, because it is slower and entirely hand-burnished by a skilled installer. Microcement can be more efficient to install over larger areas. In both cases, the installer is the biggest factor in whether the finish lasts.