benefit of perlin noise over value noise
The benefit of perlin noise is the overall distribution of frequencies. Since value noise uses simple values that are interpolated, there is a higher chance, that a row of several values only differs a little. The consequence is, that some regions of your picture may contain little changes and some regions a lot of changes. 

By using gradients you are reducing this effect because the interpolation is not done by value but instead calculated between tangents. Now it's more difficult to have a flat curve (both tangents must be collinear).



Source: As noted by Martin Ender the question was already posted on a different StackExchange community: see this Math.SE post.