As to which one is "better" I cannot say. The Corian is a completely synthetic material, while the Micarta is partly synthetic and partly natural. (glue -- linen).
If you want a smooth texture, Corian is probably best, but paper Micarta is smooth also. If you want a rougher finish that provides a better wet grip, then linen or canvas Micarta.
I'm a bit like Durulz in that I prefer wood, or at least the looks of wood. That said, there is probably no wood that would be as serviceable as Micarta. The likelihood of Micarta breaking is considerably less than wood.
I once had a horn handled knife that my mother tossed into the kitchen sink to wash for me, and forgot it and it laid all night in water, and puffed up and was ruined.
I'm going to get a knife blank and put some micarta scales on it, just to give it a fair test, but my heart is with a nicely figured piece of wood.
It is mostly a matter of asthetics. There are good hard woods like arctic birch, or bois d'arc that are practically indestructible -- but none of them are as tough as micarta / corian. For me, it all boils down to how does it look and feel, and would it be likely to fail on me? Just follow your bliss.