Cotton wrinkles if you use it. Linen wrinkles if you look at it.
Linen stays off your skin better when it's hot.
Cotton is hydrophilic, meaning it soaks up liquid (sweat, rain) and doesn't release it quickly. Not sure about linen.
Neither fabric is great at retaining colour in the long run IMHO.
Cotton/linen mixes are cool because of their rough, coarse surface.
I've just started to think why I bother ironing my linen shirts.