I paint on both cotton and linen and my personal preference at the moment is actually the cotton canvas. Why? A canvas made of cotton has a finer structure while linen normally has a rougher and sometimes a more uneven surface (think about a pair of cotton versus linen trousers and I think you'll get my point). If you paint very thin layers and small details as I do you will still see the structure of the canvas under the color. I think the end-result is nicer when the structure of the canvas doesn't steal too much attention from the motive.
If you want to overcome the problem with a rough structure, you can prime your canvas with gesso (a thick white paste). At the moment, the method I use is to paint an under-layer with acrylic color before I start with the oil, but this layer is so thin that it doesn't cover the structure (hence I opt for the cotton canvas). Important to mention is that all the canvases, (cotton as well as linen) you buy in hobby stores such as Panduro, Clas Ohlson etc. are already primed and theoretically you can start painting with oil directly on them if you prefer to do that.
To sum up, you don't always need to go for the more exclusive and expensive material. Think about the result you want to achieve and then choose your canvas!