My understanding is that ApproxFun moved away from the Chebfun-style differentiation matrices, in which you take a function in the basis of Chebyshev polynomials and represent the derivative in the same basis. The problem is that this results in dense (mostly nonzero) differentiation matrices that don’t scale well to large problems.
Instead, they represent the function and its derivative in different bases (e.g. Chebyshev and ultraspherical polynomials, respectively), and this allows the resulting derivative matrix to be sparse (banded). See these operators and this paper.
(But there’s probably a way to get the Chebfun-style matrices if you dig deep enough in the package.)