Corian is little bit different from Micarta.
It's sort of heavy, smooth and without "layers". Corian is more like fine powder (Aluminium Tri Hydrate) mixed with epoxy(PMMA) in ratio 2:1 (respectively). Sort of sleek (very smooth) and seamless. Not brittle for sure, but I really don't know how you define durability

, it doesn't suffer from age degradation (liquidation of Corian means either to burn it or ground it to powder to recyclate it into other Corian

). physical attributes are similar to those of hard wood. Chemically stable and nonabsorbing, however concentrated acids and localized heat (above 200C) can cause surface cosmetic taints.
Micarta has the nature of compressed epoxied layers of cloth paper and similar materials, unlike very uniform nature of Corian (where is instead ATH powder). Micarta can usually withstand higher temperatures (Corian can handle about 150C without any problems, above 200C can affect appearance, even higher temps can cause deformation), but is little bit surface-absorbent, but still chemically stable. In dependence on epoxy used it may be age degrading (epoxy dissolvment due to UV light).
Another thing to mention is that "micarta" can be of various composition, dependant of manufacturer/maker, but Corian's composition (or LG's alternative HI-MACS) is still the same (OK, similar

, it depends what kind (color, style) you want).
Hope this helps.