Your main point about vector fields is that vectors near each other are fairly similar. Now, assuming we have well-behaved functions that do follow that behavior, one way of "capitalizing on the similarity of a vector field" is to simply "zoom out" by taking the average of all vectors within a certain area and getting the average vector in the center of the area. This will yield a vector field with less vectors, which, because of our approximations, stand for a generalized behavior.
If, in the same scenario, we wished to emphasize the differences, then I'd suggest rather than taking an average vector for a rectangular area, you may want to divvy up your vector field such that there are regions defined by a 'central' vector and some range of tolerance from it.
However, what I think you are looking for is simply the divergence. Given your vector field $\vec F(x, y)$, making a contour plot of $D(x, y) = \nabla \cdot \vec F(x, y)$ and then choosing values of $D$ to be the contours, you can demonstrate how similar the direction and magnitude of a vector is by each curve's spacing. This also causes a loss of information, which is what you were looking for.