Linen is more expensive and has a reputation for quality so artists will list specifically that they painted on linen. If you are stretching it yourself, it is harder to stretch to an even tension and large canvases require some strength to stretch.
Linen is available in a wider range of weaves than cotton - finer weaves for a very smooth surface for fine detail painting or very rough weaves for more expressive work. Linen is stronger so will withstand rougher painting methods and heavyweight linen is a good choice for very large canvases because a large canvas requires a larger amount of tension to be taut and weak canvas could tear.
Traditionally linen was also preferred over cotton because it is a less absorbent material and as a result less likely to change tension due to atmospheric conditions.