The biggest and most readily noticeable difference will be in build quality. My Tamron 28-75 2.8 lens is great for the money. Good optics and fast constant aperture, but the build quality leaves alot to be desired. The focusing ring will sometimes move after I let go of it and I will have to adjust it again and get it to stay put. This is not good. A "pro" lens such as my Canon 17-40 L 4.0 has very good damping in the focus ring and focusing is easy, reliable and accurate. That alone is worth it for me.
Then, you have the superior optics which is not readily noticeable in a 4x6 or 5x7 print, but when you enlarge your images to 20x28, you will sure notice a difference in sharpness, contrast, and even bg blur (bokeh).
I agree with what Sebastien said in that there is a disconnect in that people do not always recognize these diffeences. I have been to exhibits where I have seen a photo enlarged to poster size that just looked awful. It should never have been enlarged because it could not stand the enlargement technically. It may have looked fine at 8x10, but the optics were not good enough to enlarge the image past that. This photographer could not see that. A pro needs to have all the benefits that a good lens will give them: Build quality, performance and optics.
Like everything else, you get what you pay for.